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Algebra 1 : Polynomials

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Example Questions

Example Question #2 : Binomials

Expand:

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

Possible Answers:

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

$2\frac{2}{3}x^3-\frac{4}{9}x^2+8x+1\frac{1}{3}$

$2\frac{2}{3}x^3+\frac{4}{9}x^2-8x+1\frac{1}{3}$

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x-1\frac{1}{3}$

$-2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

Correct answer:

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

Explanation:

First, FOIL:

$\frac{1}{3}(8x^3-\frac{4}{3}x^2-24x+\frac{12}{3})$

Simplify:

$\frac{1}{3}(8x^3-\frac{4}{3}x^2-24x+4)$

Distribute the $\frac{1}{3}$ through the parentheses:

$\frac{8}{3}x^3-\frac{4}{9}x^2-\frac{24}{3}x+\frac{4}{3}$

Rewrite to make the expression look like one of the answer choices:

$2\frac{2}{3}x^3-\frac{4}{9}x^2-8x+1\frac{1}{3}$

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Example Question #3 : How To Multiply Binomials With The Distributive Property

$\textup{If }x^{2}+4x+3=0 \textup{ , what are the possible values of }x\textup{?}$

Possible Answers:

4, 3

1,3

-3, 1

-3, -1

-1, 3

Correct answer:

-3, -1

Explanation:

$\textup{Factor the quadratic into two binomials.}$ $\, \:\left( x+a\right )\left ( x+b\right )$

$\textup{The sum of the missing numbers is the coefficient of }4x$ .

$\textup{The product of these numbers is the constant in the quadratic.}$

$a+b=4\:\:\:a\times b=3\:\:\textup{Therefore, }a\textup{ and }b\textup{ are 1 and 3.}$

$\left ( x+3\right )\left ( x+1\right )=0\:\:\:x= -3\textup{ or }-1$

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Example Question #2 : How To Multiply Binomials With The Distributive Property

Expand:

(4x-1)(-2x+3)

Possible Answers:

$8x^{2}+10x-3$

None of the other answers are correct.

$-8x^{2}+10x-3$

$-8x^{2}+14x-3$

$8x^{2}+14x-3$

Correct answer:

$-8x^{2}+14x-3$

Explanation:

Use the FOIL method, which stands for First, Inner, Outer, Last:

(4x)(-2x)+(4x)(3)+(-1)(-2x)+(-1)(3)

= -8x^2+12x+2x-3

$=-8x^{2}+14x-3$

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Example Question #3 : Binomials

Using the distributive property, simplify the following:

4(3x^2+5x-2)

Possible Answers:

7x^2+9x-6

0.75x^2+0.8x-0.5

7x^2+9x+2

12x^2+20x+8

12x^2+20x-8

Correct answer:

12x^2+20x-8

Explanation:

The distributive property is handy to help get rid of parentheses in expressions. The distributive property says you "distribute" the multiple to every term inside the parentheses. In symbols, the rule states that

a(b+c)=ab+ac

So, using this rule, we get 4(3x^2+5x-2) =4*3x^2+4*5x-4*2) = 12x^2+20x-8

Thus we have our answer is 12x^2+20x-8 .

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Example Question #2 : Binomials

Expand:

(x-9)(3x+2)

Possible Answers:

None of the other answers

$3x^{2}-25x-18$

$3x^{2}-29x-18$

$3x^{2}-18x-29$

$3x^{2}-18x-25$

Correct answer:

$3x^{2}-25x-18$

Explanation:

To multiple these binomials, you can use the FOIL method to multiply each of the expressions individually.This will give you

(x)(3x)+(x)(2)+(-9)(3x)+(-9)(2)

or $3x^{2}-25x-18$ .

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Example Question #2 : How To Multiply Binomials With The Distributive Property

Multiply: (x+9)(8-x)

Possible Answers:

-x^2-17x+72

-x^2+x+72

-x^2-x+72

-x^2-17x-72

x^2-x-72

Correct answer:

-x^2-x+72

Explanation:

In order to multiply the binomials, we will need to multiply each term of the first binomial with the terms of the second binomial.

(x+9)(8-x) = (x)(8)+(x)(-x)+(9)(8)+(9)(-x)

Simplify each term.

8x-x^2+72-9x

Combine like terms and reorder the powers from highest to lowest order.

The answer is: -x^2-x+72

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Example Question #1 : How To Multiply Binomials With The Distributive Property

Multiply the binomials: (3-x)(y-z)

Possible Answers:

3y+3z-xy+xz

3y-3z-xy+xz

3y-3z+xy+xz

3y+xz

3y-xy+xz

Correct answer:

3y-3z-xy+xz

Explanation:

Multiply each term of the first binomial with the terms of the second binomial.

(3)(y)+(3)(-z)+(-x)(y)+(-x)(-z)

Simplify the terms of this expression.

3y-3z-xy+xz

There are no like terms to simplify.

The answer is: 3y-3z-xy+xz

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Example Question #1 : Binomials

Multiply: (9-2x)(3+6x)

Possible Answers:

-12x^2-48x+12

-8x^2+48x+27

-12x^2-48x+27

-12x^2+48x+27

-4x^2+48x+27

Correct answer:

-12x^2+48x+27

Explanation:

Multiply each term of the first binomial with the second binomial and add the terms.

9(3+6x) +(-2x)(3+6x)

Simplify by distribution.

27+54x-6x-12x^2

Combine like-terms.

27+48x-12x^2

The answer is: -12x^2+48x+27

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Example Question #8 : How To Multiply Binomials With The Distributive Property

Simplify the following expression.

$(-x+10)(3x^{2}-4)$

Possible Answers:

$27x^{2}+4x-40$

$-3x^{3}+30x^{2}+4x-40$

$-3x^{3}+34x^{2}+40$

None of the other answers

$3x^{3}+30x^{2}+4x+40$

Correct answer:

$-3x^{3}+30x^{2}+4x-40$

Explanation:

$(-x+10)(3x^{2}-4)$

Use the FOIL method to multiply the binomials given.

F: $-x(3x^{2})=-3x^{3}$

O: -x(-4)=4x

I: $10(3x^{2})=30x^{2}$

L: 10(-4)=-40

Group any like terms (none for this problem) when putting all the terms back together.

$-3x^{3}+30x^{2}+4x-40$

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Example Question #1 : How To Simplify Binomials

Solve for :

3x +8 = 6x-4

Possible Answers:

x=4

$x=\frac{4}{3}$

x=-3

$x=\frac{2}{3}$

Correct answer:

x=4

Explanation:

In simplifying these two binomials, you need to isolate to one side of the equation. You can first add 4 from the right side to the left side:

3x +8 = 6x-4

3x +12 = 6x

Next you can subtract the from the left side to the right side:

12 = 3x

Finally you can divide each side by 3 to solve for :

4=x

You can double check this answer by plugging 4 into each binomial and confirm that they are equal to one another.

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Algebra 1 : Polynomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2 : Binomials

Example Question #3 : How To Multiply Binomials With The Distributive Property

Example Question #2 : How To Multiply Binomials With The Distributive Property

Example Question #3 : Binomials

Example Question #2 : Binomials

Example Question #2 : How To Multiply Binomials With The Distributive Property

Example Question #1 : How To Multiply Binomials With The Distributive Property

Example Question #1 : Binomials

Example Question #8 : How To Multiply Binomials With The Distributive Property

Example Question #1 : How To Simplify Binomials

All Algebra 1 Resources

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