Factoring a GCF From an Expression

Factor a Greatest Common Factor (GCF) from each expression.

Click "Show Answer" underneath the problem to see the answer. Or click the "Show Answers" button at the bottom of the page to see all the answers at once.

If you need assistance with a particular problem, click the "step-by-step" link for an in depth solution.

Example:

Equation: 4x^3 + 2x^2 + 2x
Answer: 2x(2x^2 + x + 1)

Quiz:

1. Equation: x^3 + x^2 + x
Answer: x(x^2 +  x + 1)
2. Equation: 15a + 12b + 6c
Answer: 3(5a + 4b + 2c)
3. Equation: 8x^2 - 18y^2
Answer: 2(4x^2 - 9y^2)
4. Equation: x^2y + 2y
Answer: y(x^2 + 2)
5. Equation: z^3 + 4z^2
Answer: z^2(z + 4)
6. Equation: 4x^2 - 4x
Answer: 4x(x - 1)
7. Equation: 15x^2 - 50x - 10
Answer: 5(3x^2 - 10x - 2)
8. Equation: 121a - 11b
Answer: 11(11a - b)
9. Equation: 64c^3 - 56c^2 + 88c
Answer: 8c(8c^2 - 7c + 11)
10. Equation: 10 - 10n + 10n^2
Answer: 10(1 - n + n^2)
11. Equation: 18k + 36k^2 + 9k^3
Answer: 9k(2 + 4k + k^2)
12. Equation: 33q^3 + 33q^2r + 33qr^2
Answer: 33q(q^2 + qr + r^2)
13. Equation: 18kxy + 4xy + 2k^2xy
Answer: 2xy(9k + 2 + k^2)
14. Equation: a^3b^2 + a^3b^4 + ab^4
Answer: ab^2(a^2 + a^2b^2 + b^2)
15. Equation: 7m + 7n + 7o
Answer: 7(m + n + o)
16. Equation: 6q + 10q^2 + 8q^3
Answer: 2q(3 + 5q + 4q^2)
17. Equation: c^3 - 5c
Answer: c(c^2 - 5)
18. Equation: k^4 + 2k^3 + 3k^2 + 4k
Answer: k(k^3 + 2k^2 + 3k + 4)
19. Equation: 14dj + 14ej
Answer: 14j(d + e)
20. Equation: m^3n^2 - m^2n^3
Answer: m^2n^2(m - n)

Related Pages

Factoring a GCF From an Expression Lesson
Brush up on your knowledge of the techniques needed to solve problems on this page.

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