Polynomials & Quadratics - SAT Math

Card 0 of 236

Question

Given and find .

$\A=x^2+2 \B=4x^2-1$

Answer

To find the sum of two polynomials first set up the operation and identify the like terms.

$\A=x^2+2 \B=4x^2-1$

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -1}$

$\x^2+4x^2=5x^2 \2+(-1)=1$

Therefore, the sum of these polynomials is,

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Question

Given and find .

$\A=x^2+2 \B=4x^2-1$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=x^2+2 \B=4x^2-1$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$A-B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} --1}$

$\x^2-4x^2=-3x^2 \2-(-1)=3$

Therefore, the sum of these polynomials is,

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Question

Given and find .

$\A=x^2+2 \B=4x^2-1$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=x^2+2 \B=4x^2-1$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$B-A={\color{Red} 4x^2}{\color{Blue} -1}{\color{Red} -x^2}{\color{Blue} -2}$

$\4x^2-x^2=3x^2 \-1-2=-3$

Therefore, the sum of these polynomials is,

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Question

If $A=3x^{3}+x+2$ , and $B=4x^{3}-2x-1$ , what is the value of

Answer

In order to find the sum of two polynomials, we must first set up the operation and identify the like terms.

$\A=3x^3+x+2 \B=4x^3-2x-1$

The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

$\3x^3+4x^3=7x^3 \x-2x=-x \2-1=1$

The sum of these polynomials is equal to the following expression:

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Question

Given and find .

$\A=3x^3+x+2 \B=4x^3-2x-1$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=3x^3+x+2 \B=4x^3-2x-1$

The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

Remember to distribute the negative sign to all terms within the parentheses.

$A-B={\color{Red} 3x^3}{\color{Blue} +x}+2{\color{Red} -4x^3}{\color{Blue} +2x}+1$

$\3x^3-4x^3=-x^3 \x+2x=3x \2+1=3$

Therefore, the sum of these polynomials is,

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Question

Answer

In order to find the difference of two polynomials, first identify like terms. The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

$\begin{array}{r}\phantom{(}4x^3-2x-1\phantom{)} \-(3x^3+\phantom{0}x+2) \ \hline \end{array}$

Remember, distribute the negative sign to all terms within the parentheses.

$\begin{array}{r}4x^3-2x-1 \+-3x^3-\phantom{0}x-2 \ \hline \end{array}$

Solve.

$\begin{array}{r}4x^3-2x-1 \+-3x^3-\phantom{0}x-2 \ \hline x^3-\phantom{0}3x-3 \end{array}$

The correct answer is .

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Question

Given and find .

$\A=2x^2+2 \B=4x^2-2$

Answer

To find the sum of two polynomials first set up the operation and identify the like terms.

$\A=2x^2+2 \B=4x^2-2$

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -2}$

$\2x^2+4x^2=6x^2 \2+(-2)=0$

Therefore, the sum of these polynomials is,

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Question

Given and find .

$\A=2x^2+2 \B=4x^2-2$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=2x^2+2 \B=4x^2-2$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$A-B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} +2}$

$\2x^2-4x^2=-2x^2 \2+2=4$

Therefore, the sum of these polynomials is,

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Question

Given and find .

$\A=2x^2+2 \B=4x^2-2$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=2x^2+2 \B=4x^2-2$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$B-A= {\color{Red} 4x^2}-2{\color{Red} -2x^2}-2$

$\4x^2-2x^2=2x^2 \-2-2=-4$

Therefore, the sum of these polynomials is,

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Question

Given and find .

$\A=x^2 \B=4x^2-1$

Answer

To find the sum of two polynomials first set up the operation and identify the like terms.

$\A=x^2 \B=4x^2-1$

The like terms in these polynomials are the squared variable.

$A+B={\color{Red} x^2}{\color{Red} +4x^2}-1$

$\x^2+4x^2=5x^2 \0+(-1)=-1$

Therefore, the sum of these polynomials is,

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Question

Given and find .

$\A=x^2+1 \B=4x^2-1$

Answer

To find the product of two polynomials first set up the operation.

$\A=x^2+1 \B=4x^2-1$

Now, multiply each term from the first polynomial with each term in the second polynomial.

Remember the rules of exponents. When like base variables are multiplied together their exponents are added together.

$\x^2\cdot 4x^2=4x^{2+2}=4x^4 \x^2\cdot -1=-x^2 \1\cdot 4x^2=4x^2 \1\cdot -1=-1$

Therefore, the product of these polynomials is,

Combine like terms to arrive at the final answer.

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Question

If and , what is $A\cdot B$ ?

Answer

To find the product of two polynomials, first set up the operation.

$\A=2x^2+2 \B=4x^2-2$

$A\cdot B=(2x^2+2)(4x^2-2)$

Now, multiply each term in the first polynomial by each term in the second polynomial. One way to remember to work through this type of multiplication is by using the acronym FOIL: First, Outside, Inside, Last. You multiply the first numbers in each parenthetical with one another, then the numbers on the outside of the entire list (the first number in the first parenthetical and the last one in the second parenthetical), then the inside numbers (the two middle ones, the last number in the first parenthetical and the first number in the second parenthetical), and finally the last numbers in each parenthetical.

$A\cdot B=(2x^2\cdot 4x^2)+(2x^2\cdot-2)+(2\cdot4x^2)+(2\cdot-2)$

When exponential terms with the same bases are multiplied together, you add the exponents.

$(2x^2\cdot 4x^2)+(2x^2\cdot-2)+(2\cdot4x^2)+(2\cdot-2)=8x^4-4x^2+8x^2-4$

Combine like terms to arrive at the solution.

When the two polynomials are multiplied together, they equal .

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Question

Given and find .

$\A=x^2+2 \B=4x^2-1$

Answer

To find the sum of two polynomials first set up the operation and identify the like terms.

$\A=x^2+2 \B=4x^2-1$

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -1}$

$\x^2+4x^2=5x^2 \2+(-1)=1$

Therefore, the sum of these polynomials is,

Compare your answer with the correct one above

Question

Given and find .

$\A=x^2+2 \B=4x^2-1$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=x^2+2 \B=4x^2-1$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$A-B={\color{Red} x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} --1}$

$\x^2-4x^2=-3x^2 \2-(-1)=3$

Therefore, the sum of these polynomials is,

Compare your answer with the correct one above

Question

Given and find .

$\A=x^2+2 \B=4x^2-1$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=x^2+2 \B=4x^2-1$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign through to all terms in the second polynomial.

$B-A={\color{Red} 4x^2}{\color{Blue} -1}{\color{Red} -x^2}{\color{Blue} -2}$

$\4x^2-x^2=3x^2 \-1-2=-3$

Therefore, the sum of these polynomials is,

Compare your answer with the correct one above

Question

If $A=3x^{3}+x+2$ , and $B=4x^{3}-2x-1$ , what is the value of

Answer

In order to find the sum of two polynomials, we must first set up the operation and identify the like terms.

$\A=3x^3+x+2 \B=4x^3-2x-1$

The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

$\3x^3+4x^3=7x^3 \x-2x=-x \2-1=1$

The sum of these polynomials is equal to the following expression:

Compare your answer with the correct one above

Question

Given and find .

$\A=3x^3+x+2 \B=4x^3-2x-1$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=3x^3+x+2 \B=4x^3-2x-1$

The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

Remember to distribute the negative sign to all terms within the parentheses.

$A-B={\color{Red} 3x^3}{\color{Blue} +x}+2{\color{Red} -4x^3}{\color{Blue} +2x}+1$

$\3x^3-4x^3=-x^3 \x+2x=3x \2+1=3$

Therefore, the sum of these polynomials is,

Compare your answer with the correct one above

Question

Answer

In order to find the difference of two polynomials, first identify like terms. The like terms in these polynomials are the squared variable, the single variable, and the constant terms.

$\begin{array}{r}\phantom{(}4x^3-2x-1\phantom{)} \-(3x^3+\phantom{0}x+2) \ \hline \end{array}$

Remember, distribute the negative sign to all terms within the parentheses.

$\begin{array}{r}4x^3-2x-1 \+-3x^3-\phantom{0}x-2 \ \hline \end{array}$

Solve.

$\begin{array}{r}4x^3-2x-1 \+-3x^3-\phantom{0}x-2 \ \hline x^3-\phantom{0}3x-3 \end{array}$

The correct answer is .

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Question

Given and find .

$\A=2x^2+2 \B=4x^2-2$

Answer

To find the sum of two polynomials first set up the operation and identify the like terms.

$\A=2x^2+2 \B=4x^2-2$

The like terms in these polynomials are the squared variable and the constant terms.

$A+B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} +4x^2}{\color{Blue} -2}$

$\2x^2+4x^2=6x^2 \2+(-2)=0$

Therefore, the sum of these polynomials is,

Compare your answer with the correct one above

Question

Given and find .

$\A=2x^2+2 \B=4x^2-2$

Answer

To find the difference of two polynomials first set up the operation and identify the like terms.

$\A=2x^2+2 \B=4x^2-2$

The like terms in these polynomials are the squared variable and the constant terms.

Remember to distribute the negative sign to all terms in the second polynomial.

$A-B={\color{Red} 2x^2}{\color{Blue} +2}{\color{Red} -4x^2}{\color{Blue} +2}$

$\2x^2-4x^2=-2x^2 \2+2=4$

Therefore, the sum of these polynomials is,

Compare your answer with the correct one above

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