# Factoring a GCF From an Expression

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

## Checking Your Answers

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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