4.12 Practice Question Solutions

1. The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, [latex]4x^2[/latex] and [latex]−9y^2[/latex] don’t have a common factor, but the whole polynomial is still factorable: [latex]4x^2−9y^2=(2x+3y)(2x−3y)[/latex].

3. Divide the [latex]x[/latex] term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

5. [latex]7m[/latex]

7. [latex]10m^3[/latex]

9. [latex]y[/latex]

11. [latex](2a−3)(a+6)[/latex]

13. [latex](3n−11)(2n+1)[/latex]

15. [latex](p+1)(2p−7)[/latex]

17. [latex](5h+3)(2h−3)[/latex]

19. [latex](9d−1)(d−8)[/latex]

21. [latex](12t+13)(t−1)[/latex]

23. [latex](4x+10)(4x−10)[/latex]

25. [latex](11p+13)(11p−13)[/latex]

27. [latex](19d+9)(19d−9)[/latex]

29. [latex](12b+5c)(12b−5c)[/latex]

31. [latex](7n+12)^2[/latex]

33. [latex](15y+4)^2[/latex]

35. [latex](5p−12)^2[/latex]

37. [latex](x+6)(x^2−6x+36)[/latex]

39. [latex](5a+7)(25a^2−35a+49)[/latex]

41. [latex](4x−5)(16x^2+20x+25)[/latex]

43. [latex](5r+12s)(25r^2−60rs+144s^2)[/latex]

45. [latex](2c+3)^\frac{−1}{4}(−7c−15)[/latex]

47. [latex](x+2)^\frac{−2}{5}(19x+10)[/latex]

49. [latex](2z−9)^\frac{−3}{2}(27z−99)[/latex]

51. [latex](14x−3)(7x+9)[/latex]

53. [latex](3x+5)(3x−5)[/latex]

55. [latex](2x+5)^2(2x−5)^2[/latex]

57. [latex](4z^2+49a^2)(2z+7a)(2z−7a)[/latex]

59. [latex]\frac{1}{(4x+9)(4x−9)(2x+3)}[/latex]