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ACT Math : Polynomials

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Add Trinomials

8x+7y+6z+7y+8z+6x=

Possible Answers:

x/14+y/14+z/14

14x+14y+14z

14x+y+z

x+y+z

42(x+y+z)

Correct answer:

14x+14y+14z

Explanation:

Like terms can be added together: is added to , is added to , and is added to . The resulting answer choice that is correct is 14x+14y+14z .

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Example Question #1 : How To Add Trinomials

Choose the answer which best simplifies the following expression:

$(10x^{2} + 5x - 5) + (3x^2 - 4x + 8)$

Possible Answers:

7x^2 + 5x - 3

13x^2 + x + 3

13x^2 + x - 3

13x^2 + 5x - 3

7x^2 + x + 3

Correct answer:

13x^2 + x + 3

Explanation:

To solve this problem simply remove the parentheses and add the like terms:

$(10x^{2} + 5x - 5) + (3x^2 - 4x + 8)$

10x^2 + 3x^2 +5x-4x-5+8

13x^2 +x + 3

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Example Question #3 : How To Add Trinomials

Choose the answer which best simplifies the following expression:

(12p^2 + 3p -12) + (-3p^2 - p +10)

Possible Answers:

9p^2 +2p -2

9p^2 - 2p + 2

9p^2 +2p -10

9p^2 - p +2

9p^2 +2p -12

Correct answer:

9p^2 +2p -2

Explanation:

To simplify, remove parentheses and combine like terms:

(12p^2 +3p -12) + (-3p^2 - p +10)

12p^2 -3p^2 +3p - p -12 +10

9p^2 +2p-2

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Example Question #4 : How To Add Trinomials

Choose the answer which best simplifies the following expression:

(q^2 +4q + 8) + (2q^2 -2q - 8)

Possible Answers:

3q^2 +4q

3q^2 +2q + 0

3q^2 -2q

3q^2 +2q - 0

3q^2 +2q

Correct answer:

3q^2 +2q

Explanation:

To simplify, remove parentheses and combine like terms:

q^2 + 4q + 8 + 2q^2 -2q - 8

q^2 + 2q^2 +4q - 2q +8 - 8

3q^2 +2q

Note that adding or subtracting a zero to the end of this equation is unnecessary.

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Example Question #5 : How To Add Trinomials

Choose the answer which best simplifies the following expression:

(4y^2 +2y + 6) + (y^2 +3y - 10)

Possible Answers:

5y^2 +5y +4

5y^2 +5y-4

5y^2 -5y -4

3y^2 + 3y -4

3y^2 - 3y + 4

Correct answer:

5y^2 +5y-4

Explanation:

To simplify, simply remove the parentheses and combine like terms:

(4y^2 +2y +6) + (y^2 +3y -10)

4y^2 +y^2 +2y +3y +6 -10

5y^2 +5y - 4

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Example Question #671 : Algebra

A hockey team has 12 forwards, 6 defensemen, and 2 goalies. When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)? F=Forward, D = Defensemen, G= Goalie

Possible Answers:

4 F, 3 D, 2 G

15 F, 8 D, 3 G

9 F, 4 D, 1 G

6 F, 2 D, 1 G

36 F, 12 D, 2 G

Correct answer:

9 F, 4 D, 1 G

Explanation:

We can represent this as a subtraction of trinomials.

(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.

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Example Question #2162 : Act Math

You go to the grocery store and pick up apples, peaches, and oranges. Today you had some friends over who ate apples, peaches, and oranges. Which of the following represents how many of each you now have left if = apples, = peaches, and = oranges?

Possible Answers:

4A+3B+3C

7A+12B+12C

6A+12B+4C

4A+3B+12C

Correct answer:

4A+3B+12C

Explanation:

1. Represent the situation with two sets of trinomials:

Before your friends ate the fruit:

7A+ 12B+16C

The fruit your friends ate:

3A+9B+4C

2. Subtract the first trinomial from the second trinomial:

(7A+12B+16C)-(3A+9B+4C)=

7A-3A+12B-9B+16C-4C=4A+3B+12C

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Example Question #2 : How To Subtract Trinomials

Choose the answer which best simplifies the following expression:

(2n^ 2 - 4n + 16) - (3n^2 + 4n -12)

Possible Answers:

-n^2 + 8n +28

-n^2 -8n +4

-n^2 +8n -28

-n^2 - 8n + 28

n^2 + 8n +28

Correct answer:

-n^2 - 8n + 28

Explanation:

To solve this expression, merely remove the parentheses (bearing in mind that because the second trinomial is being subtracted, it will be negative) and combine like terms:

(2n^ 2 - 4n + 16) - (3n^2 + 4n -12)

2n^ 2 -4n + 16 -3n^2 -4n +12

2n^2 -3n^2 -4n -4n +16 +12

-n^2 -8n +28

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Example Question #2164 : Act Math

Choose the answer which best simplifies the following expression:

(5r^2 +3r - 5) - (4r^2+5r - 8)

Possible Answers:

-r^2 -2r +3

r^2 +2r +3

r^2 +2r -3

r^2 -2r - 3

r^2 -2r +3

Correct answer:

r^2 -2r +3

Explanation:

To simplify, remove parentheses and combine like terms:

5r^2 +3r - 5 -4r^2 -5r +8

5r^2 -4r^2 +3r-5r-5+8

r^2 -2r +3

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Example Question #672 : Algebra

Choose the answer which best simplifies the following expression:

(m^2 +2m + 2) - (3m^2 -2m + 4)

Possible Answers:

2m^2 -4m + 2

-2m^2 +4m -2

m^2 +4m -2

2m^2 - 2m + 2

-2m^2 -4m -2

Correct answer:

-2m^2 +4m -2

Explanation:

To simplify, remove parentheses and combine like terms:

m^2 +2m +2 -3m^2 +2m -4

m^2 -3m^2 +2m +2m +2 -4

-2m^2 +4m -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 : How To Add Trinomials

Example Question #1 : How To Add Trinomials

Example Question #3 : How To Add Trinomials

Example Question #4 : How To Add Trinomials

Example Question #5 : How To Add Trinomials

Example Question #671 : Algebra

Example Question #2162 : Act Math

Example Question #2 : How To Subtract Trinomials

Example Question #2164 : Act Math

Example Question #672 : Algebra

All ACT Math Resources

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