# Factoring Completely

Factor each expression completely.

## Checking Your Answers

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

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