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High School Math : Pre-Algebra

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Example Questions

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

Simplify:

$x^{8}\cdot x^{5}$

Possible Answers:

$x^{13}$

$x^{40}$

$x^{8}$

$x^{35}$

Correct answer:

$x^{13}$

Explanation:

When multiplying variables, you add the exponents of each like-termed variable together to find the answer.

In this example, the exponents are and so 8+5=13 .

Our answer is $x^{13}$ .

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Example Question #12 : How To Multiply Polynomials In Pre Algebra

Combine into a single simplified fraction:

$\frac{x+3}{x+2}+\frac{x+5}{x^{2}-1}$

Possible Answers:

$\frac{4x^{3}-5x^{2}+3x-7}{-x^{3}+2x^{2}-x+2}$

$\frac{3x^{3}-2x^{2}-5x+6}{x^{3}-2x^{2}+x-2}$

$\frac{5x^{3}+3x^{2}-2x+1}{x^{3}+2x^{2}-x+2}$

$\frac{2x^{3}+2x^{2}+3x+8}{x^{3}+2x^{2}+x+2}$

$\frac{x^{3}+4x^{2}+6x+7}{x^{3}+2x^{2}-x-2}$

Correct answer:

$\frac{x^{3}+4x^{2}+6x+7}{x^{3}+2x^{2}-x-2}$

Explanation:

Multiply to get a common denominator:

$\frac{x+3}{x+2}+\frac{x+5}{x^{2}-1} = \frac{(x+3)(x^{2}-1)+(x+5)(x+2)}{(x+2)(x^{2}-1)}$

Next, using FOIL (first, outer, inner, last) remove the parantheses and then combine like terms to get:

$\frac{x^{3}+4x^{2}+6x+7}{x^{3}+2x^{2}-x-2}$

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Example Question #591 : Pre Algebra

Simplify $ax(bx-ca^{2})$ .

Possible Answers:

$abx^{2}-a^{3}cx$

2abx-3acx

$abx^{2}-ca^{2}$

$abx^{2}+ca^{3}x$

$ax-ca^{3}x$

Correct answer:

$abx^{2}-a^{3}cx$

Explanation:

Use the distributive property:

$ax(bx-ca^{2})= ax\cdot bx-ax\cdot ca^{2}= abx^{2}-a^{3}cx$

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Example Question #592 : Pre Algebra

Multiply to find the polynomial.

(2x+2)(x-4)

Possible Answers:

2x^2-6x-8

2(x^2+2x+3)

2x^2-6x+8

2x^2+6x+8

2x^2+6x-8

Correct answer:

2x^2-6x-8

Explanation:

Multiply using the FOIL method.

First: (2x)(x)=2x^2

Outside: (2x)(-4)=-8x

Inside: (x)(2)=2x

Last: (2)(-4)=-8

Add the terms together to get the final expression.

2x^2-8x+2x-8=2x^2-6x-8

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Example Question #593 : Pre Algebra

Multiply to find the polynomial.

(x+2)(-x-7)

Possible Answers:

-x^2+9x+14

x^2-9x-14

-x^2+9x-14

x^2+9x+14

-x^2-9x-14

Correct answer:

-x^2-9x-14

Explanation:

Multiply using the FOIL method.

First: (x)(-x)=-x^2

Outside: (x)(-7)=-7x

Inside: (2)(-x)=-2x

Last: (2)(-7)=-14

Add the terms to get the final expression.

-x^2-7x-2x-14=-x^2-9x-14

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Example Question #594 : 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 #595 : Pre Algebra

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

Possible Answers:

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

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

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

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

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

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:

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

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

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

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

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

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 #2 : How To Divide Polynomials In Pre Algebra

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

Possible Answers:

$x^{18}$

$x^{5}$

$x^{45}$

$x^{12}$

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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High School Math : Pre-Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #12 : How To Multiply Polynomials In Pre Algebra

Example Question #591 : Pre Algebra

Example Question #592 : Pre Algebra

Example Question #593 : Pre Algebra

Example Question #594 : Pre Algebra

Example Question #595 : Pre Algebra

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

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

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

All High School Math Resources

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