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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #53 : Distributive Property

Simplify:

$y=\frac{(x^2-16)(x+7)}{x+4}+(x-1)^2+13$

Possible Answers:

y=2x^2+x-14

y=2(x^2+x-7)

$y=\frac{x^3+7x^2-16x-112}{x+4}+(x-1)^2+13$

$y=\frac{(x^2-16)(x+7)}{x+4}+x^2-2x+14$

y=x^2-x-14

Correct answer:

y=2x^2+x-14

Explanation:

$y=\frac{(x^2-16)(x+7)}{x+4}+(x-1)^2+13$

First, factor the numerator of the quotient term by recognizing the difference of squares:

$y=\frac{(x-4)(x+4)(x+7)}{x+4}+(x-1)^2+13$

Cancel out the common term from the numerator and denominator:

y=(x-4)(x+7)+(x-1)^2+13

FOIL (First Outer Inner Last) the first two terms of the equation:

y=x^2+7x-4x-28+x^2-2x+1+13

Combine like terms:

y=2x^2+x-14

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Example Question #2 : Write A Polynomial Function From Its Zeros

Create a cubic function that has roots at x=2,-3,0 .

Possible Answers:

f(x)=x^3+2x^2-6x

f(x)=x^3+2x^2-5x

f(x)=x^3+x^2-6x

f(x)= x^3+3x^2-2x^2-6x

f(x)=x^3+x^2-5x

Correct answer:

f(x)=x^3+x^2-6x

Explanation:

x=0, x=2, x=-3

This can be written as:

x=0, x-2=0, x+3=0

Multiply the terms together:

f(x)= x(x-2)(x+3)

Multiply the first two terms:

f(x)=(x^2-2x)(x+3),

FOIL:

f(x)= x^3+3x^2-2x^2-6x

Combine like terms:

f(x)=x^3+x^2-6x

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Example Question #31 : Simplifying Expressions

Evaluate the following to its simplest form:

$\frac{1}{2}(4x+2)(x-2)+\frac{1}{3}(2x-3)$

Possible Answers:

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

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

None of the available answers

$4x^2-2\frac{1}{3}x-3$

$2x^2-2\frac{2}{3}x-3$

Correct answer:

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

Explanation:

$\frac{1}{2}(4x+2)(x-2)+\frac{1}{3}(2x-3)$

First we will foil the first function before distributing.

$\frac{1}{2}(4x^2-8x+2x-4)+\frac{1}{3}(2x-3)$

$\frac{1}{2}(4x^2-6x-4)+\frac{1}{3}(2x-3)$

We will then distribute out the $\frac{1}{2}$

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

We will then distribute out the $\frac{1}{3}$

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

Now the only like terms we have are $-3x+\frac{2}{3}x$ and -2-1 , so our final answer is:

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

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Example Question #72 : Expressions

Simplify the expression: 6(4k+8s)

Possible Answers:

32ks

24k+8s

24k+48s

72ks

10k+14s

Correct answer:

24k+48s

Explanation:

distributes to , multiplying to become 24k , and distributes to , multiplying to make 48s .

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Example Question #11 : Foil

Use FOIL to distribute the following:

(4x-3)(3x+4)

Possible Answers:

$12x^{2}+7x-12$

$12x^{2}-7x-12$

$12x^{2}+25x-12$

$12x^{2}-25x-12$

$12x^{2}+25x+12$

Correct answer:

$12x^{2}+7x-12$

Explanation:

Make sure you keep track of negative signs when doing FOIL, especially when doing the Outer and Inner steps.

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Example Question #12 : Foil

Use FOIL to distribute the following:

(2x-3)(2x+3)

Possible Answers:

$4x^{2}+6x-9$

$4x^{2}-12x-9$

$4x^{2}+9$

$4x^{2}-9$

$4x^{2}+12x-9$

Correct answer:

$4x^{2}-9$

Explanation:

When the 2 terms differ only in their sign, the -term drops out from the final product.

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Example Question #63 : Distributive Property

Solve: (x+2)(x-16)

Possible Answers:

x^2+14x-32

x^2-32x-32

x^2-18x-32

x^2+18x-32

x^2-14x-32

Correct answer:

x^2-14x-32

Explanation:

To solve this, use the FOIL method.

(a+b)(c+d)= ac+ad+bc+bd

Follow suit for (x+2)(x-16) .

=x^2+(x)(-16)+(2)(x)+(2)(-16)

=x^2-16x+2x-32

Combine like terms and simplify.

x^2-14x-32

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Example Question #64 : Distributive Property

Multiply the binomials using the FOIL method.

(x+8)(x-3)

Possible Answers:

$x^{2}-5x-24$

$x^{2}+5x-24$

$x^{2}+24$

$x^{2}-3x+8$

Correct answer:

$x^{2}+5x-24$

Explanation:

Using the FOIL method:

First terms multiplied: $x^{2}$

Outer terms: -3x

Inner terms:

Last terms:

Added together, they make the polynomial $x^{2}+5x-24$

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Example Question #65 : Distributive Property

Use the FOIL method to simplify: (2x-6)(x+2)

Possible Answers:

2x^2+10x-12

2x^2+2x-12

2x^2-10x-12

2x^2-10x+12

2x^2-2x-12

Correct answer:

2x^2-2x-12

Explanation:

Use the following formula as an approach to FOIL method.

(a+b)(c+d)= ac+ad+bc+bd

(2x-6)(x+2)=(2x)(x)+(2x)(2)+(-6)(x)+(-6)(2)

Simplify and combine like terms.

2x^2+4x-6x-12 = 2x^2-2x-12

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Example Question #63 : Distributive Property

Use the FOIL method to distribute the following expression.

(2x+4)(3x+6)

Possible Answers:

6x^2+19x+12

6x^2+12x+24

6x^2+24x+24

12x^2+24x+24

12x^2+3x+4

Correct answer:

6x^2+24x+24

Explanation:

FOIL is a method used for distribution. It stands for first, outer, inner, and last. First you multiply the first terms, in this case and . Next the first term and the outer term and . Then, the inner terms and . Finally, the last terms and . This will give you the expression 6x^2+12x+12x+24 . When simplified the expression becomes 6x^2+24x+24 .

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #53 : Distributive Property

Example Question #2 : Write A Polynomial Function From Its Zeros

Example Question #31 : Simplifying Expressions

Example Question #72 : Expressions

Example Question #11 : Foil

Example Question #12 : Foil

Example Question #63 : Distributive Property

Example Question #64 : Distributive Property

Example Question #65 : Distributive Property

Example Question #63 : Distributive Property

All Algebra 1 Resources

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