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High School Math : Polynomials

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Example Questions

Example Question #71 : Polynomials

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

Possible Answers:

$x^{16}$

$x^{144}$

$x^{7}$

$x^{25}$

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 #1 : How To Divide Polynomials In Pre Algebra

Divide the quadratic expression.

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

Possible Answers:

6x^3+2x-1

6x^2+2x-2

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 #72 : Polynomials

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

Possible Answers:

$x^{ 3}$

$x^{15}$

$x^{31 }$

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

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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Example Question #73 : Polynomials

Simplify:

$\frac{x+4}{x^{2}+7x+12}$

Possible Answers:

$\frac{1}{x^{2}-12}$

$\frac{4}{7x+12}$

$\frac{1}{x^{2}+7x+3}$

$\frac{1}{x-4}$

$\frac{1}{x+3}$

Correct answer:

$\frac{1}{x+3}$

Explanation:

Use FOIL to factor the denominator, and then check if any factors cancel:

$\frac{x+4}{x^{2}+7x+12} = \frac{x+4}{(x+3)(x+4)}=\frac{1}{x+3}$

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Example Question #1 : How To Solve A Polynomial In Pre Algebra

Solve $x^{3}=125$

Possible Answers:

x=15

x=5

x=25

x=75

Correct answer:

x=5

Explanation:

To solve an equation with we must take the cube root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt[3]{x^{3}}=\sqrt[3]{125}$

Then we perform the cube root to get the answer x=5 .

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Example Question #1 : How To Solve A Polynomial In Pre Algebra

Solve $x^{2}=64$

Possible Answers:

x=32

x=8

x=64

$x=\pm8$

Correct answer:

$x=\pm8$

Explanation:

To solve an equation with we must take the square root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt{x^{}2}=\sqrt{64}$

Then we perform the square root to get the answer x=8

Remember that squared can also equal so our answer will be both positive and negative.

The final answer looks like $x=\pm8$

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Example Question #3 : How To Solve A Polynomial In Pre Algebra

Solve $x^{3}= 125$

Possible Answers:

x=15

x=25

x=5

x=12

Correct answer:

x=5

Explanation:

To solve an equation with we must take the cube root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt[3]{x^3}=\sqrt[3]{125}$

Then we perform the cube root to get the answer x=5 .

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Example Question #4 : How To Solve A Polynomial In Pre Algebra

Sovle $x^{2}=144$ .

Possible Answers:

$x=\pm4$

x=12

$x=\pm12$

$x=\pm6$

Correct answer:

$x=\pm12$

Explanation:

To solve an equation with $x^{2}$ we must take the square root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt{x^{2}}=\sqrt{144}$

Then we perform the square root to get the answer $x=\pm12$

Remember that $-12^{2}$ can also equal 144 so our answer will be both positive and negative.

The final answer looks like $x=\pm12$ .

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Example Question #5 : How To Solve A Polynomial In Pre Algebra

Solve for if, $x^{4}=256$

Possible Answers:

$\pm16$

$\pm8$

$\pm2$

$\pm4$

Correct answer:

$\pm4$

Explanation:

To solve an equation with we must take the quad root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt[4]{x^{4}}=\sqrt[4]{256}$

Then we perform the quad root to get the answer x=4

Remember that $(-4)^{4}$ can also equal 256 so our answer will be both positive and negative.

The final answer looks like $x=\pm4$ .

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Example Question #6 : How To Solve A Polynomial In Pre Algebra

Solve for if, $x^{2}=121$

Possible Answers:

$x=\pm13$

$x=\pm12$

$x=\pm15$

$x=\pm11$

Correct answer:

$x=\pm11$

Explanation:

To solve an equation with we must take the square root of each side of the equation to get by itself.

Doing this makes our problem look like $\sqrt{x^{2}}=\sqrt{121}$

Then we perform the square root to get the answer x=11

Remember that $(-11)^{2}$ can also equal 121 so our answer will be both positive and negative.

The final answer looks like $x=\pm11$ .

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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 #71 : Polynomials

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

Example Question #72 : Polynomials

Example Question #73 : Polynomials

Example Question #1 : How To Solve A Polynomial In Pre Algebra

Example Question #1 : How To Solve A Polynomial In Pre Algebra

Example Question #3 : How To Solve A Polynomial In Pre Algebra

Example Question #4 : How To Solve A Polynomial In Pre Algebra

Example Question #5 : How To Solve A Polynomial In Pre Algebra

Example Question #6 : How To Solve A Polynomial In Pre Algebra

All High School Math Resources

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