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)
Show step-by-step

Quiz:

  1. Equation: x^3 - x 

  2. Equation: x^3 + 5x^2 + 6x 

  3. Equation: 4y^2 - 8y - 60 

  4. Equation: 3q^2 - 12q + 12 

  5. Equation: 3m^3 + 33m^2 + 90m 

  6. Equation: 4x^2 + 8xy + 4y^2 

  7. Equation: 4kx^2 - 4ky^2 

  8. Equation: m^4 - 1 
    Answer:  = (m + 1)(m - 1)(m^2 + 1)
    Hide answer|Show step-by-step 

  9. Equation: p^4 - 2p^2 + 1 
    Answer:  = (p - 1)(p + 1)(p + 1)(p - 1)
    Hide answer|Show step-by-step 

  10. Equation: abc^2 + 6abc + 5ab 

  11. Equation: 24x^2 + 68x + 48 

  12. Equation: 4x^2y + 12xy^2 + 9y^3 

  13. Equation: 3mx^2 - 5mx - 28m 

  14. Equation: 21k - 98k^2 - 343k^3 

  15. Equation: 4p^4 - 5p^2 + 1 
    Answer:  = (2p + 1)(2p - 1)(p + 1)(p - 1)
    Hide answer|Show step-by-step 

  16. Equation: 36r^4 + 29r^2 - 20 
    Answer:  = (3r + 2)(3r - 2)(4r^2 + 5)
    Hide answer|Show step-by-step 

  17. Equation: 108s^6 + 42s^4 - 6s^2 
    Answer:  = 6s^2(3s + 1)(3s - 1)(2s^2 + 1)
    Hide answer|Show step-by-step 

  18. Equation: 144uv^4 - 388uv^2 + 144u 
    Answer:  = 4u(2v + 3)(2v - 3)(3v + 2)(3v - 2)
    Hide answer|Show step-by-step 

  19. Equation: 6m^3n - 9m^2n^2 - 15mn^3 

  20. Equation: 2p^3x + p^2x - 28px

Show all answers

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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