# Factoring Completely

Factor each expression completely.

Enter an answer in each box, then click the “Show Answers” button at the bottom of the page to see the answers.

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

## Example:

`Equation: x^4 + 7x^3 + 12x^2 `
`Answer:  = x^2(x + 3)(x + 4)`

## Quiz:

1. `Equation: x^3 - x `
`Answer:  = x(x - 1)(x + 1)`

2. `Equation: x^3 + 5x^2 + 6x `
`Answer:  = x(x + 2)(x + 3)`

3. `Equation: 4y^2 - 8y - 60 `
`Answer:  = 4(y + 3)(y - 5)`

4. `Equation: 3q^2 - 12q + 12 `
`Answer:  = 3(q - 2)(q - 2)`

5. `Equation: 3m^3 + 33m^2 + 90m `
`Answer:  = 3m(m + 5)(m + 6)`

6. `Equation: 4x^2 + 8xy + 4y^2 `
`Answer:  = 4(x + y)(x + y)`

7. `Equation: 4kx^2 - 4ky^2 `
`Answer:  = 4k(x + y)(x - y)`

8. `Equation: m^4 - 1 `
`Answer:  = (m + 1)(m - 1)(m^2 + 1)`

9. `Equation: p^4 - 2p^2 + 1 `
`Answer:  = (p - 1)(p + 1)(p + 1)(p - 1)`

10. `Equation: abc^2 + 6abc + 5ab `
`Answer:  = ab(c + 1)(c + 5)`

11. `Equation: 24x^2 + 68x + 48 `
`Answer:  = 4(2x + 3)(3x + 4)`

12. `Equation: 4x^2y + 12xy^2 + 9y^3 `
`Answer:  = y(2x + 3y)(2x + 3y)`

13. `Equation: 3mx^2 - 5mx - 28m `
`Answer:  = m(3x + 7)(x - 4)`

14. `Equation: 21k - 98k^2 - 343k^3 `
`Answer:  = 7k(1 - 7k)(3 + 7k)`

15. `Equation: 4p^4 - 5p^2 + 1 `
`Answer:  = (2p + 1)(2p - 1)(p + 1)(p - 1)`

16. `Equation: 36r^4 + 29r^2 - 20 `
`Answer:  = (3r + 2)(3r - 2)(4r^2 + 5)`

17. `Equation: 108s^6 + 42s^4 - 6s^2 `
`Answer:  = 6s^2(3s + 1)(3s - 1)(2s^2 + 1)`

18. `Equation: 144uv^4 - 388uv^2 + 144u `
`Answer:  = 4u(2v + 3)(2v - 3)(3v + 2)(3v - 2)`

19. `Equation: 6m^3n - 9m^2n^2 - 15mn^3 `
`Answer:  = 3mn(m + n)(2m - 5n)`

20. `Equation: 2p^3x + p^2x - 28px `
`Answer:  = px(p + 4)(2p - 7)`

## Related Pages

Factoring Completely Lesson

Brush up on your knowledge of the techniques needed to solve problems on this page.

Expression Factoring Calculator

Simplifies and factors expressions automatically.

## Tutoring

Looking for someone to help you with algebra? At Wyzant, connect with algebra tutors and math tutors nearby. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of clicks.

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