Factoring Out the GCF

Show your work for each problem.

1.
What is the GCF of and ?
1. a)
2. b)
3. c)
4. d)
Answer:
The GCF of 6 and 9 is 3. Since has no , we cannot include in the GCF. The answer is .
2.
Factor:
1. a)
2. b)
3. c)
4. d)
Answer:
The GCF of 4 and 8 is 4. Dividing: and . So .
3.
What is the GCF of and ? (Write your answer like: 5x)
Answer: 5x
GCF of 10 and 15 is 5. Both terms have , and the lowest power is . So the GCF is .
4.
Factor . Write only what's inside the parentheses after factoring.
Answer: x + 2
GCF = 6. Dividing: and . So . Inside the parentheses: .
5.
Factor:
Answer: 5(2x + 3)
1. What is the GCF of 10 and 15? 5
2. What is ? 2x
3. What is ? 3
6.
What is the GCF of and ?
1. a)
2. b)
3. c)
4. d)
Answer:
GCF of 8 and 12 is 4. The lowest power of is . So the GCF is .
7.
Factor completely:
1. a)
2. b)
3. c)
4. d)
Answer:
GCF of 6 and 9 is 3. Both terms have , so we include . GCF = . Dividing: , . Answer: .
8.
Factor . Write the GCF only (like: 4x^2)
Answer: 4x^2
GCF of 12 and 8 is 4. The lowest power of is . So the GCF is . Full answer: .
9.
Factor . Write the full factored form (like: 5x(3x-2))
Answer: 5x(3x - 2)
GCF of 15 and 10 is 5. Both terms have . GCF = . Dividing: , . Answer: .
10.
Factor:
Answer: 6x^2(3x + 4)
1. What is the GCF of 18 and 24? 6
2. What is the lowest power of in both terms? x^2
3. So the complete GCF is? 6x^2
4. What is ? 3x
11.
Factor:
Answer: 7(2x^2 + 3x - 1)
1. What is the GCF of 14, 21, and 7? 7
2. Do all terms have a common variable? (yes/no) no
3. What is ? 2x^2
4. What is ? 3x
12.
Factor:
1. a)
2. b)
3. c)
4. d)
Answer:
GCF: 10 (from 20 and 30), (lowest power of ), (lowest power of ). GCF = . Answer: .
13.
Factor: . Write the full factored form.
Answer: 6ab^2(4ab - 3)
GCF: 6 (numbers), (lowest power), (lowest power). GCF = . Dividing: , . Answer: .
14.
Factor: . Factor out a negative GCF.
Answer: -4x(3x - 2)
GCF magnitude is . Factoring out : , . Answer: .
15.
Factor:
Answer: 12x^2y(3x^2y^2 + 4xy - 1)
1. What is the GCF of 36, 48, and 12? 12
2. What is the lowest power of across all three terms? x^2
3. What is the lowest power of across all three terms? y
4. So the complete GCF is? 12x^2y
16.
Factor: . Factor out a negative GCF.
Answer: -5x(3x^2 + 5x - 2)
1. What is the GCF of 15, 25, and 10? 5
2. What is the lowest power of ? x
3. Since the leading term is negative, the GCF we factor out is? -5x
4. What is ? 3x^2