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High School Math : How to divide polynomials in pre-algebra

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Example Questions

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:

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

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

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

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

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

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 #1 : How To Divide Polynomials In Pre Algebra

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

Possible Answers:

$x^{5}$

$x^{18}$

$x^{45}$

$x^{12}$

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 #1 : 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:

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

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

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

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

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

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 #3 : How To Divide Polynomials In Pre Algebra

Simplify:

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

Possible Answers:

$4y^{12}$

$4y^{6}$

$6y^{6}$

$4y^{3}$

$6y^{3}$

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 #2 : How To Divide Polynomials In Pre Algebra

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

Possible Answers:

$x^{4}$

$x^{3}$

x^5

$x^{2}$

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 #3 : How To Divide Polynomials In Pre Algebra

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 #5 : How To Divide Polynomials In Pre Algebra

Simplify the expression.

$15y^2\div 3y$

Possible Answers:

12y^3

5y^3

-5y

12y

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

Simplify $\frac{x^{16}}{x^{9}}$ .

Possible Answers:

$x^{7}$

$x^{144}$

$x^{16}$

$x^{25}$

Correct answer:

$x^{7}$

Explanation:

When dividing monmials with the same base, you subtract the power of the numerator by the power of the denominator 16-9=7

The answer, , is the power of the simplified expression.

In this example our answer is $x^{7}$ .

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

Divide the quadratic expression.

$\frac{8x^4+4x^2-2x}{2x}$

Possible Answers:

6x^2+2x-2

6x^3+2x-1

4x^2+2x-2

4x^3+2x-1

Correct answer:

4x^3+2x-1

Explanation:

$\frac{8x^4+4x^2-2x}{2x}$

We can think of this expression in terms of the distributive property, allowing us to break it into individual terms.

$\frac{1}{2x}(8x^4+4x^2-2x)$

$\frac{8x^4}{2x}+\frac{4x^2}{2x}-\frac{2x}{2x}$

Using this method, we can cancel the $\small 2x$ from each term to get our final answer.

4x^3+2x-1

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Example Question #5 : How To Divide Polynomials In Pre Algebra

Simplify $\frac{x^{17}}{x^{14}}$

Possible Answers:

$x^{31 }$

$x^{ 3}$

$x^{15}$

$x^{\frac{17}{14}}$

Correct answer:

$x^{ 3}$

Explanation:

When dividing like-termed variables, you subtract the power of the numerator by the power of the denominator.

The power of the simplified expression will be 17-14=3

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

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High School Math : How to divide polynomials in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

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

Example Question #2 : How To Divide Polynomials In Pre Algebra

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

Example Question #5 : How To Divide Polynomials In Pre Algebra

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

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

Example Question #5 : How To Divide Polynomials In Pre Algebra

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