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High School Math : Pre-Algebra

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Example Questions

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 #601 : Pre Algebra

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

Possible Answers:

$x^{3}$

$x^{4}$

$x^{2}$

x^5

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 #602 : Pre Algebra

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

Possible Answers:

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

$x^{9}$

$x^{25}$

$x^{11}$

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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Example Question #603 : Pre Algebra

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

Possible Answers:

$x^{144}$

$x^{7}$

$x^{16}$

$x^{25}$

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 #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 #604 : Pre Algebra

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

Possible Answers:

$x^{31 }$

$x^{15}$

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

$x^{ 3}$

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 #11 : How To Divide Polynomials In Pre Algebra

Simplify:

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

Possible Answers:

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

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

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

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

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

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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High School Math : Pre-Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

Example Question #601 : Pre Algebra

Example Question #602 : Pre Algebra

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

Example Question #603 : Pre Algebra

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

Example Question #604 : Pre Algebra

Example Question #11 : How To Divide Polynomials In Pre Algebra

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

All High School Math Resources

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