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15k^3 - 2k^2 - k 36. a^2b^2 - a^2 Factor each polynomial, if possible. If the polynomial cannot be...

35. 15k^3 - 2k^2 - k
36. a^2b^2 - a^2
Factor each polynomial, if possible. If the polynomial cannot be factored, write prime.
25. 4k^2 - 100
26. 9x^2 - 3x - 20
27. x^2 + 6x - 9
28. 50g^2 + 40g + 8
29. 9t^3 + 66t^2 - 48t
30. 4a^2 - 36b^2
31. 20n^2 + 34n + 6
32. 5y^2 - 90
33. 24x^3 - 78x^2 + 45x
34. 18y^2 - 48y + 32
35. 90g - 27g^2 - 75
36. 45c^2 - 32cd
37. 4a^3 + 3a^2b + 8a + 6b^2
38. 5a^2 + 7a + 6b^2 - 4b
39. x^3y^2 - y^2 - z^2 + x^2z^2
40. 4m^4n + 6m^3n - 16m^2n^2 - 24mn^2
7) 27m^3 - 125
8) x^3 - 64

Answer

  1. 15k^3 - 2k^2 - k: Factor out k: k(15k^2 - 2k - 1).

  2. a^2b^2 - a^2: Factor out a^2: a^2(b^2 - 1). Further factor as a^2(b - 1)(b + 1).

  3. 4k^2 - 100: Difference of squares: (2k - 10)(2k + 10).

  4. 9x^2 - 3x - 20: Factor as (3x + 5)(3x - 4).

  5. x^2 + 6x - 9: Prime.

  6. 50g^2 + 40g + 8: Factor out 2: 2(25g^2 + 20g + 4). Further factor as 2(5g + 2)^2.

  7. 9t^3 + 66t^2 - 48t: Factor out 3t: 3t(3t^2 + 22t - 16).

  8. 4a^2 - 36b^2: Difference of squares: (2a - 6b)(2a + 6b).

  9. 20n^2 + 34n + 6: Factor as (2n + 1)(10n + 6).

  10. 5y^2 - 90: Factor out 5: 5(y^2 - 18).

  11. 24x^3 - 78x^2 + 45x: Factor out 3x: 3x(8x^2 - 26x + 15).

  12. 18y^2 - 48y + 32: Factor out 2: 2(9y^2 - 24y + 16). Further factor as 2(3y - 4)^2.

  13. 90g - 27g^2 - 75: Factor out 3: 3(-9g^2 + 30g - 25).

  14. 45c^2 - 32cd: Factor out c: c(45c - 32d).

  15. 4a^3 + 3a^2b + 8a + 6b^2: Group and factor: a^2(4a + 3b) + 2(4a + 3b). Further factor as (a^2 + 2)(4a + 3b).

  16. 5a^2 + 7a + 6b^2 - 4b: Group and factor: (5a^2 + 7a) + (6b^2 - 4b). Factor as a(5a + 7) + 2b(3b - 2).

  17. x^3y^2 - y^2 - z^2 + x^2z^2: Group and factor: y^2(x^3 - 1) - z^2(1 - x^2).

  18. 4m^4n + 6m^3n - 16m^2n^2 - 24mn^2: Factor out 2mn: 2mn(2m^3 + 3m^2 - 8mn - 12n).

  19. 27m^3 - 125: Difference of cubes: (3m - 5)(9m^2 + 15m + 25).

  20. x^3 - 64: Difference of cubes: (x - 4)(x^2 + 4x + 16).

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