Factoring by Grouping

Show your work for each problem.

1.
What is the first step in factoring by grouping?
1. a)Find the GCF of all terms
2. b)Add all coefficients
3. c)Multiply the binomials
4. d)Group the terms in pairs
Answer: Group the terms in pairs
The first step is to group the terms in pairs, typically the first two terms together and the last two terms together.
2.
When factoring , what is the GCF of the first group ?
1. a)
2. b)
3. c)
4. d)
Answer:
Both and have at least as a factor. and , so the GCF is .
3.
What is the GCF of ?
Answer: 3
Both 3 and 6 are divisible by 3. So .
4.
After factoring , what is the common binomial factor?
1. a)
2. b)
3. c)
4. d)
Answer:
Both terms have as a factor: and . So is the common binomial factor.
5.
Factor completely: . Write the answer in the form .
Answer: (x+2)(x^2+3)
Group: . Factor: . Factor out : .
6.
Factor:
Answer: (x+2)(2x^2+3)
1. What is the GCF of the first group ? 2x^2
2. After factoring out , what binomial remains? x+2
3. What is the GCF of the second group ? 3
4. What is the final factored form? (x+2)(2x^2+3)
7.
Factor:
Answer: (y+3)(x+2)
8.
Factor:
Answer: (x-2)(3x^2+5)
1. What is the GCF of ? 3x^2
2. After factoring , what binomial do you get? x-2
3. What is the GCF of ? 5
4. What is the final factored form? (x-2)(3x^2+5)
9.
When factoring , what should you factor out from the second group to match the binomial from the first group?
1. a)
2. b)
3. c)
4. d)
Answer:
Factor out from to get , which matches from the first group.
10.
Factor:
Answer: (x+2)(4x^2-1)
11.
Factor:
Answer: (2x+3)(3x^2+2)
1. What is the GCF of ? 3x^2
2. After factoring , what binomial remains? 2x+3
3. What is the GCF of ? 2
4. What is the final factored form? (2x+3)(3x^2+2)
12.
Factor:
Answer: (x+3)(2x^2-3)
1. What is the GCF of ? 2x^2
2. After factoring , what binomial remains? x+3
3. What should you factor out from to get ? -3
4. What is the final factored form? (x+3)(2x^2-3)
13.
Factor completely:
Answer: (x-2)(5x^2-3)
14.
Factor:
Answer: (y+2)(3x-5)
1. What is the GCF of ? 3x
2. After factoring , what binomial remains? y+2
3. What should you factor out from to get ? -5
4. What is the final factored form? (y+2)(3x-5)
15.
Which polynomial CANNOT be factored by grouping?
1. a)
2. b)
3. c)
4. d)
Answer:
For : . The second group has no common factor that gives , so it cannot be factored by grouping.
16.
Factor completely:
Answer: (2x+3)(4x^2-3)