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ACT Math : Polynomials

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Example Questions

Example Question #1 : Binomials And Foil

Which of the following expressions is equivalent to: 6x (m²+yx²–3)?

Possible Answers:

6xm² + 6yx² -18x

xm² + 7x³ -18

6xm² + 6yx³ -18

6xm² + 7x³ -18

6xm² + 6yx³ -18x

Correct answer:

6xm² + 6yx³ -18x

Explanation:

6x (m²+yx²–3)= 6x∙m²+ 6xyx² – 6x∙3= 6xm² + 6yx³-18x (Use Distributive Property)

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

Which of the following expressions is equivalent to: $7x(x^{2}+xz^{2}-7)$ ?

Possible Answers:

$x^{3}+x^{2}z^{2}-49x$

$7x^{3}+7x^{2}z^{2}-49$

$7x^{3}+7x^{2}z^{2}-49x$

$7x^{2}+x^{2}z^{2}-49x$

$7x^{3}+7z^{2}-49x$

Correct answer:

$7x^{3}+7x^{2}z^{2}-49x$

Explanation:

Use the distributive property to multiply by all of the terms in $(x^{2}+xz^{2}-7)$ :

$(7x\cdot x^{2})+(7x\cdot xz^{2}) + (7x\cdot -7)=$

$7x^{3}+7x^{2}z^{2}-49x$

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

If and are constants and x^2+sx+24 is equivalent to (x-4)(x-t) , what is the value of ?

Possible Answers:

Cannot be determined from the given information.

Correct answer:

Explanation:

The question gives us a quadratic expression and its factored form. From this, we know

(4)(t)=24

At this point, solve for t.

t=6

Now, we can plug in to get

(x-4)(x-6) .

Now, use FOIL to get s.

(x-4)(x-6)

=x^2-6x-4x+24

=x^2-10x+24

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Example Question #1 : Binomials And Foil

Which expression is equal to (x+1)(x-2) ?

Possible Answers:

x^2-x-2

x^2-2

2x-1

x^2-3x-2

x^2-x+2

Correct answer:

x^2-x-2

Explanation:

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

$\\F:x*x=x^2\\O: x*(-2)=-2x\\I: 1*x=x\\L:1*(-2)=-2\\ x^2-2x+x-2=x^2-x-2$

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

Which expression is equal to (x-2)(x+2) ?

Possible Answers:

x^2

2x^2+4x-1

x^2-4x-4

x^2-4

x^2+4

Correct answer:

x^2-4

Explanation:

$\\F:x*x=x^2\\O: x*2=2x\\I: (-2)*x=-2x\\L:2*(-2)=-4\\ x^2-2x+2x-4=x^2-4$

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Example Question #6 : Binomials And Foil

Which expression is equal to (x+4)(x-7) ?

Possible Answers:

x^2-3

x^2-3x-28

x^2+4x-7

2x-3

x^2+7x-4

Correct answer:

x^2-3x-28

Explanation:

$\\F:x*x=x^2\\ O: x*(-7)=-7x\\ I: 4*x=4x\\ L:4*(-7)=-28\\ x^2-7x+4x-28= x^2-3x-28$

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Example Question #7 : Binomials And Foil

Which expression is equal to (x^2+4)(x+1) ?

Possible Answers:

x^2+4x+4

x^3+2x^2+x+4

x^3+x^2+x+5

x^3+x^2+4x+4

x^2+x+5

Correct answer:

x^3+x^2+4x+4

Explanation:

$\\F:x^2*x=x^3\\ O: x^2*1=x^2\\ I: 4*x=4x\\ L:4*1=4\\ x^3+x^2+4x+4$

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

Which expression is equal to (x^2-1)(x+2) ?

Possible Answers:

x^3+1

x^3+x^2-x+2

x^3+2x^2-x-2

2x^3+3x^2-x+1

x^2+x+1

Correct answer:

x^3+2x^2-x-2

Explanation:

$\\F:x^2*x=x^3\\ O: x^2*2=2x^2\\ I: (-1)*x=-x\\ L:(-1)*2=-2\\ x^3+2x^2-x-2$

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Example Question #62 : Variables

Find the -intercepts:

$y=9-10x+x^{2}$

Possible Answers:

(0,9) only

(0,1) and (0,0)

(0,1) and (0,9)

(1,0) and (9,0)

Correct answer:

(1,0) and (9,0)

Explanation:

-intercepts occur when y=0 .

1. Set the expression equal to and rearrange:

$x^{2}-10x+9=0$

2. Factor the expression:

(x-1)(x-9)=0

3. Solve for :

x-1=0

x=1

and...

x-9=0

x=9

4. Rewrite the answers as coordinates:

x=9 becomes (9,0) and x=1 becomes (1,0) .

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Example Question #63 : Variables

Solve for when $6x^{2}+2x-20=0$ .

Possible Answers:

x=0, x=-2

x=0, x=4

$x=\frac{-5}{3}, x=2$

$x=\frac{5}{3}, x=-2$

Correct answer:

$x=\frac{5}{3}, x=-2$

Explanation:

1. Factor the expression:

$6x^{2}+2x-20= (3x-5)(2x+4)$

2. Solve for :

3x-5=0

$x=\frac{5}{3}$

and...

2x+4=0

x=-2

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ACT Math : Polynomials

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Binomials And Foil

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

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

Example Question #1 : Binomials And Foil

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

Example Question #6 : Binomials And Foil

Example Question #7 : Binomials And Foil

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

Example Question #62 : Variables

Example Question #63 : Variables

All ACT Math Resources

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