Algebra Quiz: Terms Factors And Coefficients
20 questions · exam conditions
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Terms Factors And CoefficientsQuestion 1 of 20

What is the coefficient of yy in the expression 2y2−y+62y^2-y+6?

22
−1-1
11
−y-y
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Algebra Quiz

Algebra Quiz: Terms Factors And Coefficients

Practice Terms Factors And Coefficients in Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Terms Factors And Coefficients, giving you a quick way to practice the rules, question types, and explanations that matter most for Algebra.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

What is the coefficient of yy in the expression 2y2−y+62y^2-y+6?

  1. 22
  2. −1-1 (correct answer)
  3. 11
  4. −y-y
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of y in 2y² - y + 6, we look for the term that contains y (without higher powers). That term is -y. The coefficient is the number part that's multiplied by the variable, which is -1. If you don't see a number written, like in just 'x', the coefficient is 1! Choice B is correct because it properly identifies the coefficient as -1, following the definition that 'invisible' coefficients include the sign. You've got it! Choice C misses that when we don't see a number, like in '-y', there's still a coefficient—it's -1. These 'invisible' coefficients are easy to overlook! To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 2

In the expression (x+4)(x−2)(x + 4)(x - 2), what are the factors?

  1. x+4x−2x+4x-2
  2. x, 4, x, −2x,\ 4,\ x,\ -2
  3. (x+4) and (x−2)(x+4)\ \text{and}\ (x-2) (correct answer)
  4. x+4, x, −2x+4,\ x,\ -2
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify factors. Factors are parts of an expression that are multiplied together: when you see multiplication (either with · or parentheses next to each other), you're looking at factors. For example, in 4(x + 3), the factors are 4 and (x + 3) because they're being multiplied. In (x + 4)(x - 2), we can see what's being multiplied together: it's (x + 4) times (x - 2). This means the factors are (x + 4) and (x - 2). Remember, factors are connected by multiplication, while terms are connected by addition and subtraction. Choice A is correct because it properly identifies the factors as (x + 4) and (x - 2), following the definition that factors are the multiplied parts. You've got it! Choice B is close, but it confuses terms with factors: it lists x, 4, x, -2 which are terms inside the parentheses, but the question asks for the main factors. Remember: terms are added/subtracted, factors are multiplied! Think of terms as 'ingredients being added together' and factors as 'ingredients being multiplied together.' In (x + 4)(x - 2), you're multiplying (x + 4) times (x - 2), so those are factors. But when you expand to x² + 2x - 8, you're adding x², 2x, and -8, so those are terms. Choice D treats parts inside parentheses as separate terms, but actually (x + 4) is grouped as one factor here. Terms are only separated by + and - at the outermost level!

Question 3

What is the coefficient of aa in the expression −5a+2a2−1-5a+2a^2-1?

  1. −5-5 (correct answer)
  2. 22
  3. 55
  4. −5a-5a
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x23x^2, the coefficient is 3 because it's the number being multiplied by x2x^2. Remember that coefficients include their sign, so in −5x-5x, the coefficient is -5, not 5. To find the coefficient of aa in −5a+2a2−1-5a + 2a^2 - 1, we look for the term that contains aa. That term is −5a-5a. The coefficient is the number part that's multiplied by the variable, which is -5 with the sign. Choice A is correct because it properly identifies the coefficient as -5, following the definition that coefficients include their sign. You've got it! Choice B is close, but it forgets to include the sign: the coefficient is -5, not 5. The minus sign is part of the coefficient! This is a super common mistake, so watch out for it. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like aa) or -1 (for terms like −a-a). Write out that 'invisible 1' when learning, and it'll help!

Question 4

In the expression −x+9-x+9, what is the coefficient of xx?

  1. 11
  2. −1-1 (correct answer)
  3. −x-x
  4. 99
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of x in -x + 9, we look for the term that contains x. That term is -x. The coefficient is the number part that's multiplied by the variable, which is -1. If you don't see a number written, like in just '-x', the coefficient is -1! Choice B is correct because it properly identifies the coefficient as -1, following the definition that coefficients include their sign. You've got it! Choice A is close, but it misses that when we don't see a number, like in '-x', there's still a coefficient—it's -1, not 1. These 'invisible' coefficients are easy to overlook! To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 5

What are the terms in 3x2−5x+23x^2-5x+2?

  1. 3x2,  5x,  23x^2,\;5x,\;2
  2. 3x2,  −5x,  23x^2,\;-5x,\;2 (correct answer)
  3. 3,  x2,  −5,  x,  23,\;x^2,\;-5,\;x,\;2
  4. 3x2−5x,  23x^2-5x,\;2
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x² - 5x + 2, there are three terms: 3x², -5x, and 2 (notice that the -5x includes the minus sign). Let's look at the expression 3x² - 5x + 2 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have 3x², then -5x, and finally +2. That gives us 3 terms total. Choice B is correct because it properly identifies the terms as 3x², -5x, 2, following the definition that terms include their signs. You've got it! Choice A is close, but it forgets to include the sign: the term is -5x, not 5x. The minus sign is part of the term! This is a super common mistake, so watch out for it. Don't forget: signs matter! The term in x² - 4x isn't 4x, it's -4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!

Question 6

What is the coefficient of the quadratic term in the expression 4−2x+9x24 - 2x + 9x^2?

  1. 99 (correct answer)
  2. −2-2
  3. 9x29x^2
  4. 44
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of the quadratic term in 4 - 2x + 9x², we look for the term that contains x² (the quadratic). That term is +9x². The coefficient is the number part that's multiplied by the variable, which is 9 (with sign, but it's positive). If you don't see a number written, like in just 'x', the coefficient is 1! Choice A is correct because it properly identifies the coefficient as 9, following the definition that it's the numerical multiplier of the x² term. You've got it! Choice C is close, but it gives the entire term 9x² when the question asks just for the coefficient (which would be 9, the number part). The coefficient is only the numerical part, not the variable. Choice B forgets that the quadratic term is 9x² with coefficient 9, not -2 (which is for the x term). This is a super common mistake, so watch out for it. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 7

What is the constant term in 3k3−2k2+k3k^3-2k^2+k?

  1. kk
  2. 00 (correct answer)
  3. 33
  4. −2-2
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify the constant term. The constant term is the part of the expression that doesn't have any variables—it's just a number by itself, like the +2 at the end of 3x² - 5x + 2. The constant term is the number that stands alone without any variables attached. In 3k³ - 2k² + k, looking through each part, there is no constant term, so it's 0. This is different from the coefficients, which are the numbers multiplied by variables. Choice B is correct because it properly identifies the constant term as 0, following the definition that it's the number without variables. You've got it! Choice C forgets that the constant term is the number without any variables. In this expression, there's none, so 0, not 3 (which is a coefficient). A quick check: count your terms by counting how many parts would be separated if you put the expression in a calculator with clear + and - between them. For 3k³ - 2k² + k, you'd enter it as three separate chunks—all with variables, so constant is 0!

Question 8

What is the coefficient of xx in the expression x+5x+5?

  1. 00
  2. 11 (correct answer)
  3. xx
  4. 55
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of x in x + 5, we look for the term that contains x. That term is x (or +x). The coefficient is the number part that's multiplied by the variable, which is 1. If you don't see a number written, like in just 'x', the coefficient is 1! Choice C is correct because it properly identifies the coefficient as 1, following the definition that 'invisible' coefficients are 1. You've got it! Choice A gives 0, but that would mean no x term at all; here there is an x with coefficient 1. These 'invisible' coefficients are easy to overlook! To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 9

In the expression 6x(x−3)6x(x-3), what are the factors being multiplied?

  1. 6x6x and x−3x-3 are the terms
  2. 6x−36x-3 and xx
  3. 6x6x and (x−3)(x-3) (correct answer)
  4. 6,  x,  x,  −36,\;x,\;x,\;-3 are the terms
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify factors. Factors are parts of an expression that are multiplied together: when you see multiplication (either with · or parentheses next to each other), you're looking at factors. For example, in 4(x + 3), the factors are 4 and (x + 3) because they're being multiplied. In 6x(x - 3), we can see what's being multiplied together: it's 6x and (x - 3). This means the factors are 6x and (x - 3). Remember, factors are connected by multiplication, while terms are connected by addition and subtraction. Choice A is correct because it properly identifies the factors as 6x and (x - 3), following the definition that factors are the parts being multiplied. You've got it! Choice D confuses terms with factors: it lists 6x and x-3 as terms, but the question asks for factors. Remember: terms are added/subtracted, factors are multiplied! Think of terms as 'ingredients being added together' and factors as 'ingredients being multiplied together.' In 2(x + 3), you're multiplying 2 times (x + 3), so those are factors. But when you expand to 2x + 6, you're adding 2x and 6, so those are terms.

Question 10

What is the coefficient of xx in the expression x2−4x+1x^2 - 4x + 1?

  1. −4x-4x
  2. 44
  3. −4-4 (correct answer)
  4. 11
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the coefficient of x in x² - 4x + 1, we look for the term that contains x. That term is -4x (with sign). The coefficient is the number part that's multiplied by the variable, which is -4 (with sign). If you don't see a number written, like in just 'x', the coefficient is 1! Choice C is correct because it properly identifies the coefficient as -4, following the definition that coefficients include the sign and are the numerical multiplier. You've got it! Choice B is close, but it forgets to include the sign: the coefficient is -4, not 4. This is a super common mistake, so watch out for it. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help! Don't forget: signs matter! The term in x² - 4x isn't 4x, it's -4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!

Question 11

The cost (in dollars) to rent a bike is given by C=3h+8C=3h+8, where hh is the number of hours. What is the constant term in 3h+83h+8?

  1. 33
  2. 88 (correct answer)
  3. 3h3h
  4. hh
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify the constant term. The constant term is the part of the expression that doesn't have any variables—it's just a number by itself, like the +2 at the end of 3x² - 5x + 2. The constant term is the number that stands alone without any variables attached. In 3h + 8, looking through each part, the constant term is +8. This is different from the coefficients, which are the numbers multiplied by variables. Choice C is correct because it properly identifies the constant term as 8, following the definition that it's the number without variables. You've got it! Choice A forgets that the constant term is the number without any variables. In this expression, it's 8, not 3 (which is the coefficient of h). A quick check: count your terms by counting how many parts would be separated if you put the expression in a calculator with clear + and - between them. For 3h + 8, you'd enter it as two separate chunks connected by operations—those are your two terms, and the constant is the one without h!

Question 12

What is the constant term in −6x3+2x−8-6x^3+2x-8?

  1. −6-6
  2. 22
  3. −8-8 (correct answer)
  4. 88
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify the constant term. The constant term is the part of the expression that doesn't have any variables—it's just a number by itself, like the +2 at the end of 3x² - 5x + 2. The constant term is the number that stands alone without any variables attached. In -6x³ + 2x - 8, looking through each part, the constant term is -8. This is different from the coefficients, which are the numbers multiplied by variables. Choice C is correct because it properly identifies the constant term as -8, following the definition that it's the number without variables, including its sign. You've got it! Choice A is close, but it might confuse the coefficient of x³ with the constant; the constant is the standalone number, not attached to a variable. It's an easy mistake to make when you're learning to identify these parts! A quick check: count your terms by counting how many parts would be separated if you put the expression in a calculator with clear + and - between them. For 3x² - 5x + 2, you'd enter it as three separate chunks connected by operations—those are your three terms!

Question 13

Which of the following correctly identifies the terms in 2p3+3p−82p^3+3p-8?

  1. 2,  p3,  3,  p,  82,\;p^3,\;3,\;p,\;8
  2. 2p3,  3p,  −82p^3,\;3p,\;-8 (correct answer)
  3. 2p3,  3,  p,  −82p^3,\;3,\;p,\;-8
  4. 2p3+3p,  −82p^3+3p,\;-8
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x² - 5x + 2, there are three terms: 3x², -5x, and 2 (notice that the -5x includes the minus sign). Let's look at the expression 2p³ + 3p - 8 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have 2p³, then +3p, and finally -8. That gives us 3 terms total. Choice A is correct because it properly identifies the terms as 2p³, 3p, -8, following the definition that terms include their signs. You've got it! Choice D confuses terms with factors: it lists 2, p³, 3, p, 8 which are factors within terms, but the question asks for terms. Remember: terms are added/subtracted, factors are multiplied! Don't forget: signs matter! The term in x² - 4x isn't 4x, it's -4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!

Question 14

What are the terms in 4a2−a+74a^2 - a + 7?

  1. 4a2−a,  74a^2-a,\;7
  2. 4a2,  a,  74a^2,\;a,\;7
  3. 4a2,  −a,  74a^2,\;-a,\;7 (correct answer)
  4. 4,  a2,  −1,  a,  74,\;a^2,\;-1,\;a,\;7
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x2−5x+23x^2 - 5x + 2, there are three terms: 3x23x^2, −5x-5x, and 22 (notice that the −5x-5x includes the minus sign). Let's look at the expression 4a2−a+74a^2 - a + 7 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have 4a24a^2, then −a-a, and finally +7+7. That gives us 3 terms total. Choice A is correct because it properly identifies the terms as 4a24a^2, −a-a, 77, following the definition that terms include their signs. You've got it! Choice B is close, but it forgets to include the sign: the term is −a-a, not a. The minus sign is part of the term! This is a super common mistake, so watch out for it. Don't forget: signs matter! The term in x2−4xx^2 - 4x isn't 4x, it's −4x-4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!

Question 15

In the expression 3(x+2)3(x+2), what are the factors?

  1. 3,  x,  23,\;x,\;2 are the terms
  2. 3x3x and 22
  3. 33 and (x+2)(x+2) (correct answer)
  4. xx and 22 are the factors
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify factors. Factors are parts of an expression that are multiplied together: when you see multiplication (either with · or parentheses next to each other), you're looking at factors. For example, in 4(x + 3), the factors are 4 and (x + 3) because they're being multiplied. In 3(x + 2), we can see what's being multiplied together: it's 3 and (x + 2). This means the factors are 3 and (x + 2). Remember, factors are connected by multiplication, while terms are connected by addition and subtraction. Choice A is correct because it properly identifies the factors as 3 and (x + 2), following the definition that factors are the parts being multiplied. You've got it! Choice B confuses terms with factors: it lists 3x and 2 which would be terms if expanded, but the question asks for factors in the given form. Remember: terms are added/subtracted, factors are multiplied! Think of terms as 'ingredients being added together' and factors as 'ingredients being multiplied together.' In 2(x + 3), you're multiplying 2 times (x + 3), so those are factors. But when you expand to 2x + 6, you're adding 2x and 6, so those are terms.

Question 16

In the expression −x2+3x−4-x^2 + 3x - 4, what is the leading coefficient?

  1. −4-4
  2. −x2-x^2
  3. 33
  4. −1-1 (correct answer)
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify coefficients. A coefficient is the numerical part of a term that's multiplied by the variable(s): in the term 3x², the coefficient is 3 because it's the number being multiplied by x². Remember that coefficients include their sign, so in -5x, the coefficient is -5, not 5. To find the leading coefficient in -x² + 3x - 4, we look for the term with the highest power, which is -x² (like -1x²). That term is -x². The coefficient is the number part that's multiplied by the variable, which is -1 (with sign). If you don't see a number written, like in just 'x', the coefficient is 1! Choice B is correct because it properly identifies the leading coefficient as -1, following the definition that invisible coefficients with signs are -1 for terms like -x². You've got it! Choice D is close, but it forgets to include the sign and misses the leading term: the leading coefficient is -1 for -x², not -4 (which is the constant). This is a super common mistake, so watch out for it. Choice C gives the entire term -x² when the question asks just for the coefficient (which would be -1, the number part). The coefficient is only the numerical part, not the variable. To find a coefficient, first locate the term with the variable you're looking for, then identify just the number part (including the sign). If you don't see a number, the coefficient is 1 (for terms like x) or -1 (for terms like -x). Write out that 'invisible 1' when learning, and it'll help!

Question 17

How many terms are in the expression x2+0x−6x^2+0x-6?

  1. 22
  2. 11
  3. 33 (correct answer)
  4. 00
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x2−5x+23x^2 - 5x + 2, there are three terms: 3x23x^2, −5x-5x, and 22 (notice that the −5x-5x includes the minus sign). Let's look at the expression x2+0x−6x^2 + 0x - 6 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have x2x^2, then +0x+0x (remember to include the sign!), and finally −6-6. That gives us 3 terms total. Choice C is correct because it properly identifies 3 terms, following the definition that terms are the chunks connected by + or -. You've got it! Choice A counts only 2, but let me help clarify: even though 0x0x is zero, it's still written as a separate term here. It's an easy mistake to make when you're learning to identify these parts! Here's an easy way to identify terms: look for the + and - signs that aren't inside parentheses—those are your term separators! Everything between those signs (including the sign right before it) is one term. So in x2+0x−6x^2 + 0x - 6, circle each + and -, and you can see the three terms clearly!

Question 18

What are the terms in x3+4xx^3+4x?

  1. x3,  4xx^3,\;4x (correct answer)
  2. x,  3,  4,  xx,\;3,\;4,\;x
  3. x3+4xx^3+4x (one term)
  4. x3,  −4xx^3,\;-4x
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x² - 5x + 2, there are three terms: 3x², -5x, and 2 (notice that the -5x includes the minus sign). Let's look at the expression x³ + 4x and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have x³, then +4x. That gives us 2 terms total. Choice A is correct because it properly identifies the terms as x³, 4x, following the definition that terms include their signs (here + is implied for the first). You've got it! Choice D is close, but it incorrectly changes the sign to -4x; the expression has +4x. This is a super common mistake, so watch out for it. Don't forget: signs matter! The term in x² - 4x isn't 4x, it's -4x. Always include the sign that comes right before the term—that sign is part of it. This is one of the most common mistakes in algebra, so being careful here will save you lots of points!

Question 19

How many terms are in the expression 2x3−5x2+x−92x^3 - 5x^2 + x - 9?

  1. 4 (correct answer)
  2. 3
  3. 6
  4. 5
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x² - 5x + 2, there are three terms: 3x², -5x, and 2 (notice that the -5x includes the minus sign). Let's look at the expression 2x³ - 5x² + x - 9 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have 2x³, then -5x² (remember to include the sign!), then +x, and finally -9. That gives us four terms total. Choice B is correct because it properly identifies there are 4 terms, following the definition that terms include their signs and are separated by addition or subtraction. You've got it! Choice C is close, but it counts incorrectly, perhaps by splitting variables or signs separately; but let me help clarify: each chunk like -5x² or +x is one full term, not broken into pieces. It's an easy mistake to make when you're learning to identify these parts! A quick check: count your terms by counting how many parts would be separated if you put the expression in a calculator with clear + and - between them. For 2x³ - 5x² + x - 9, you'd enter it as four separate chunks connected by operations—those are your four terms! Here's an easy way to identify terms: look for the + and - signs that aren't inside parentheses—those are your term separators! Everything between those signs (including the sign right before it) is one term. So in 2x³ - 5x² + x - 9, circle each + and -, and you can see the four terms clearly!

Question 20

How many terms are in the expression 2x3−5x2+x−92x^3-5x^2+x-9?

  1. 33
  2. 44 (correct answer)
  3. 55
  4. 22
Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify terms. Terms are the parts of an expression that are added or subtracted from each other: think of them as the separate 'chunks' connected by + or - signs. For example, in 3x² - 5x + 2, there are three terms: 3x², -5x, and 2 (notice that the -5x includes the minus sign). Let's look at the expression 2x³ - 5x² + x - 9 and find the terms. Terms are separated by + or - signs (at the main level, not inside parentheses): starting from the left, we have 2x³, then -5x², then +x (which is 1x), and finally -9. That gives us 4 terms total. Choice B is correct because it properly identifies 4 terms, following the definition that terms are the separate parts connected by + or - signs. You've got it! Choice A is close, but it forgets to count the +x as a separate term; sometimes people miss terms with 'invisible' coefficients like 1. This is a super common mistake, so watch out for it. Here's an easy way to identify terms: look for the + and - signs that aren't inside parentheses—those are your term separators! Everything between those signs (including the sign right before it) is one term. So in 5x² - 3x + 7, circle each + and -, and you can see the three terms clearly!