0-3 Factoring Polynomials
Factor each polynomial.
2
1. 12x + 4x
SOLUTION: Use the Distributive Property to factor.
2
The GCF of 12x and 4x is 2 ∙ 2 ∙ x or 4x.
Rewrite each term using the GCF.
2
2. 6x y + 2x
SOLUTION: Use the Distributive Property to factor.
2
The GCF of 6x y and 2x is 2 ∙ x or 2x.
Rewrite each term using the GCF.
2
3. 8ab – 12ab
SOLUTION: Use the Distributive Property to factor.
2
The GCF of 8ab and 12ab is 2 ∙ 2 ∙ a ∙ b or 4ab.
Rewrite each term using the GCF.
2
4. x + 5x + 4
SOLUTION: In this trinomial, b is 5 and c is 4. Find two numbers with a product of 4 and a sum of 5.
The correct factors are 1 and 4.
2
12y + -27
5. y +Manual
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SOLUTION: In this trinomial, b is 12 and c is 27. Find two numbers with a product of 27 and a sum of 12.
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The correct factors are 1 and 4.
0-3 Factoring Polynomials
2
5. y + 12y + 27
SOLUTION: In this trinomial, b is 12 and c is 27. Find two numbers with a product of 27 and a sum of 12.
The correct factors are 3 and 9.
2
6. x + 6x + 8
SOLUTION: In this trinomial, b is 6 and c is 8. Find two numbers with a product of 8 and a sum of 6.
The correct factors are 2 and 4.
2
7. 3y + 13y + 4
SOLUTION: In this trinomial, a = 3, b = 13, and c = 4. Find two numbers with a product of 3(4) = 12 and a sum of 13.
The correct factors are 1 and 12.
2
8. 7x + 51x + 14
SOLUTION: In this trinomial, a = 7, b = 51, and c = 14. Find two numbers with a product of 7(14) = 98 and a sum of 51.
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The correct factors are 2 and 49.
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0-3 Factoring Polynomials
2
8. 7x + 51x + 14
SOLUTION: In this trinomial, a = 7, b = 51, and c = 14. Find two numbers with a product of 7(14) = 98 and a sum of 51.
The correct factors are 2 and 49.
2
9. 3x + 28x + 32
SOLUTION: In this trinomial, a = 3, b = 28, and c = 32.
Find two numbers with a product of 3(32) = 96 and a sum of 28.
The correct factors are 24 and 4.
2
10. x – 5x + 6
SOLUTION: In this trinomial, b = −5 and c = 6. This means that m + p is negative and mp is positive. So m and p must both be
negative.
The correct factors are −2 and −3.
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0-3 Factoring Polynomials
2
10. x – 5x + 6
SOLUTION: In this trinomial, b = −5 and c = 6. This means that m + p is negative and mp is positive. So m and p must both be
negative.
The correct factors are −2 and −3.
2
11. y – 5y + 4
SOLUTION: In this trinomial, b = −5 and c = 4. This means that m + p is negative and mp is positive. So, m and p must both be
negative.
The correct factors are −1 and −4.
2
12. 6x – 13x + 5
SOLUTION: In this trinomial, a = 6, b = −13, and c = 5. This means that m + p is negative and mp is positive. So m and p must
both be negative.
The correct factors are −10 and −3.
2
13. 6a – 50ab + 16b
2
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SOLUTION: Page 4
0-3 Factoring Polynomials
2
13. 6a – 50ab + 16b
2
SOLUTION: 2
14. 11x – 78x + 7
SOLUTION: In this trinomial, a = 11, b = −78, and c = 7. This means that m + p is negative and mp is positive. So m and p must
both be negative.
The correct factors are −77 and −1.
2
15. 18x – 31xy + 6y
2
SOLUTION: Factor by grouping.
2
16. x + 4xy + 4y
2
SOLUTION: This is a perfect square trinomial.
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17. 9x – 24x + 16
SOLUTION: Page 5
SOLUTION: This is a perfect square trinomial.
0-3 Factoring Polynomials
2
17. 9x – 24x + 16
SOLUTION: This is a perfect square trinomial.
2
18. 4a + 12ab + 9b
2
SOLUTION: This is a perfect square trinomial.
2
19. x – 144
SOLUTION: This polynomial can be factored as a difference of squares.
2
20. 4c – 9
SOLUTION: This polynomial can be factored as a difference of squares.
2
21. 16y – 1
SOLUTION: This polynomial can be factored as a difference of squares.
2
2
22. 25x – 4y
SOLUTION: This polynomial can be factored as a difference of squares.
2
23. 36y – 16
SOLUTION: Factor out a 4. Then factor the rest as a difference of squares.
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SOLUTION: This polynomial can be factored as a difference of squares.
0-3 Factoring Polynomials
2
23. 36y – 16
SOLUTION: Factor out a 4. Then factor the rest as a difference of squares.
2
24. 9a – 49b
2
SOLUTION: This polynomial can be factored as a difference of squares.
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