# 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