Factoring Trinomials (General)

Show your work for each problem.

1.
What is the AC product for ?
1. a)
2. b)
3. c)
4. d)
Answer:
For , we have and . The AC product is .
2.
Which pair of numbers has a product of and a sum of ?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
✓ and ✓. While , we have .
3.
For , what is the AC product?
Answer: 24
Here and . The AC product is . Note that we ignore the sign of when calculating AC.
4.
Factor . Write your answer in the form .
Answer: (2x+3)(x+1)
AC = 6. Numbers: 2 and 3 (2 + 3 = 5). Rewrite: .
5.
What is the factored form of ?
1. a)
2. b)
3. c)
4. d)
Answer:
AC = 24. Numbers 4 and 6 work: and . Rewrite: .
6.
Factor using the AC method.
Answer: (2x+1)(x+3)
1. What is ? 6
2. Find two numbers that multiply to 6 and add to 7. What are they? 1 and 6
3. Rewrite as the sum of two terms using these numbers. 1x + 6x
4. What is the final factored form? (2x+1)(x+3)
7.
Which pair of numbers has a product of and a sum of ?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
✓ and ✓. The other pairs either don't multiply to -18 or don't add to 3.
8.
Factor . Write your answer in the form .
Answer: (3x-5)(x+2)
AC = -30. Numbers: 6 and -5 (6 + (-5) = 1). Rewrite: .
9.
Factor using the AC method.
Answer: (5x+2)(x-3)
1. What is the AC product? -30
2. Find two numbers that multiply to -30 and add to -13. 2 and -15
3. Rewrite using these numbers. 2x - 15x
4. What is the final factored form? (5x+2)(x-3)
10.
Factor .
Answer: (2x-3)(2x+1)
AC = -12. Numbers: 2 and -6. Rewrite: .
11.
What is the factored form of ?
1. a)
2. b)
3. c)
4. d)
Answer:
AC = -18. Numbers 2 and -9 work: and . .
12.
Factor using the AC method.
Answer: (3x+2)(2x+5)
1. What is the AC product? 60
2. Find two numbers that multiply to 60 and add to 19. 4 and 15
3. Rewrite using these numbers. 4x + 15x
4. What is the final factored form? (3x+2)(2x+5)
13.
Factor using the AC method.
Answer: (4x-1)(2x-3)
1. What is the AC product? 24
2. Find two numbers that multiply to 24 and add to -14. -2 and -12
3. Rewrite using these numbers. -2x - 12x
4. What is the final factored form? (4x-1)(2x-3)
14.
Factor .
Answer: (3x-2)^2
AC = 36. Numbers -6 and -6. . Perfect square!
15.
Factor using the AC method.
Answer: (6x-5)(2x+3)
1. What is the AC product? -180
2. Find two numbers that multiply to -180 and add to 8. 18 and -10
3. Rewrite using these numbers. 18x - 10x
4. What is the final factored form? (6x-5)(2x+3)
16.
Factor completely: (Hint: Look for a GCF first!)
Answer: 3(2x+3)(x-4)
GCF = 3. . For : AC = -24, numbers 3 and -8. .