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High School Math : Polynomials

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Example Questions

Example Question #14 : How To Multiply Polynomials In Pre Algebra

What is $10\%$ of ?

Possible Answers:

Correct answer:

Explanation:

Convert % to a decimal, which is .

Then multiply by to get .

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Example Question #15 : How To Multiply Polynomials In Pre Algebra

What is the product of and $4x^{2}-3xy+y^{2}$ ?

Possible Answers:

$6x^{3}-x^{2}y+xy^{2}$

$6x^{3}-5x^{2}y+2xy^{2}$

$-8x^{3}+6x^{2}y-2xy^{2}$

$8x^{3}-6x^{2}y+2xy^{2}$

$2x^{3}-x^{2}y-xy^{2}$

Correct answer:

$8x^{3}-6x^{2}y+2xy^{2}$

Explanation:

In order to simplify this problem distribute to each component of $4x^{2}-3xy+y^{2}$ .

$=(2x)(4x^{2}-3xy+y^{2})$

Distribute.

$=(2x*4x^{2})+(2x*-3xy)+(2x*y^{2})$

Multiply and simplify.

$=8x^{3}-6x^{2}y+2xy^{2}$

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Example Question #18 : How To Multiply Polynomials In Pre Algebra

The length of a particular rectangle is greater than the width of the rectangle. If the perimeter of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

If the width is , then the length is x + 4 . The perimeter equals , so x + x + x+4 + x+4 = 16 .

solving for , we have 4x + 8 = 16

x = 2 , the width, so the length is .

Then, to find the area we multiply times , which equals .

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Example Question #1 : How To Divide Polynomials In Pre Algebra

Simplify $\frac{2x^{3}y^{2}}{3a^{2}b^{3}}\div \frac{6x^{2}y^{3}}{15ab^{4}}$

Possible Answers:

$\frac{3xa}{5yb}$

$\frac{5xb}{3ya}$

$\frac{2yb}{9xa}$

$\frac{5ya}{6xb}$

$\frac{9xb}{2ya}$

Correct answer:

$\frac{5xb}{3ya}$

Explanation:

Dividing by a fraction is the same as multiplying by its reciprocal:

$\frac{2x^{3}y^{2}}{3a^{2}b^{3}}\div \frac{6x^{2}y^{3}}{15ab^{4}}$ becomes $\frac{2x^{3}y^{2}}{3a^{2}b^{3}}\cdot \frac{15ab^{4}}{6x^{2}y^{3}}$

Simplify the fraction by removing factors that are common to the numerator and the denominator to get

$\frac{5xb}{3ya}$

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Example Question #61 : Polynomials

What is $\frac{x^{15}}{x^{3}}$ ?

Possible Answers:

$x^{45}$

$x^{18}$

$x^{12}$

$x^{5}$

Correct answer:

$x^{12}$

Explanation:

When dividing polynomials you subtract the power of the numerator by the power of the denominator.

The answer is the power of the simplified expression 15-3=12

In this example our answer is $x^{12}$ .

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Example Question #3 : How To Divide Polynomials In Pre Algebra

What is the quotient when $\dpi{100} 9x^{3}+24x^{2}y-21xy^{2}$ is divided by ?

Possible Answers:

$\dpi{100} 3x^{4}+8^{3}y-7x^{2}y^{2}$

$\dpi{100} 27x^{2}+72xy-63y^{2}$

$\dpi{100} 12x^{2}+27xy-24y^{2}$

$\dpi{100} -3x^{2}-8xy+7y^{2}$

$3x^{2}+8xy-7y^{2}$

Correct answer:

$3x^{2}+8xy-7y^{2}$

Explanation:

In order to simplify one must distribute the divisor into every term of the equation $\dpi{100} 9x^{3}+24x^{2}y-21xy^{2}$ .

$\dpi{100} =\frac{ 9x^{3}+24x^{2}y-21xy^{2}}{3x}$

Distribute.

$=\frac{9x^{3}}{3x}+\frac{24x^{2}y}{3x}+\frac{-21xy^{2}}{3x}$

Divide and simplify.

$=3x^{2}+8xy-7y^{2}$

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Example Question #4 : How To Divide Polynomials In Pre Algebra

Simplify:

$\frac{\8y^9 }{\2y ^3}$

Possible Answers:

$6y^{6}$

$4y^{12}$

$6y^{3}$

$4y^{6}$

$4y^{3}$

Correct answer:

$4y^{6}$

Explanation:

To divide monomials first you look at the coefficients and and perform division 8/2=4 .

To divide the exponents y^9 and y^3 you follow the laws of exponents so you subtract the exponents 9-3=6 . That leaves the answer as $4y^{6}$ .

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Example Question #62 : Polynomials

Simplify $\frac{x^{4}}{x}$

Possible Answers:

$x^{4}$

$x^{2}$

x^5

$x^{3}$

Correct answer:

$x^{3}$

Explanation:

When dividing polynomials you subtract the power of the numerator by the power of the denominator.

The answer is the power of the simplified expression in this case 4-1=3

In this example our answer is $x^{3}$ .

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Example Question #63 : Polynomials

Simplify $\frac{x^{18}}{x^{7}}$ ?

Possible Answers:

$x^{11}$

$x^{9}$

$\frac{1}{x^{11}}$

$x^{25}$

Correct answer:

$x^{11}$

Explanation:

When dividing polynomials you subtract the power of the numerator by the power of the denominator.

The answer is the power of the simplified expression 18-7=11

In this example our answer is $x^{11}$ .

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Example Question #7 : How To Divide Polynomials In Pre Algebra

Simplify the expression.

$15y^2\div 3y$

Possible Answers:

5y^3

12y

12y^3

-5y

Correct answer:

Explanation:

$15y^2\div 3y$

We can re-write this expression as a fraction.

$\frac{15y^2}{3y}$

To simplify the variable, we subtract the exponent in the denominator from the exponent in the numerator.

$\frac{15}{3}y^{2-1}$

Now we can simplify each term.

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High School Math : Polynomials

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #14 : How To Multiply Polynomials In Pre Algebra

Example Question #15 : How To Multiply Polynomials In Pre Algebra

Example Question #18 : How To Multiply Polynomials In Pre Algebra

Example Question #1 : How To Divide Polynomials In Pre Algebra

Example Question #61 : Polynomials

Example Question #3 : How To Divide Polynomials In Pre Algebra

Example Question #4 : How To Divide Polynomials In Pre Algebra

Example Question #62 : Polynomials

Example Question #63 : Polynomials

Example Question #7 : How To Divide Polynomials In Pre Algebra

All High School Math Resources

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