Solutions to Try Its

1. [latex]\left({b}^{2}-a\right)\left(x+6\right)[/latex]

2. [latex]\left(x - 6\right)\left(x - 1\right)[/latex]

3. a. [latex]\left(2x+3\right)\left(x+3\right)[/latex]
b. [latex]\left(3x - 1\right)\left(2x+1\right)[/latex]

4. [latex]{\left(7x - 1\right)}^{2}[/latex]

5. [latex]\left(9y+10\right)\left(9y - 10\right)[/latex]

6. [latex]\left(6a+b\right)\left(36{a}^{2}-6ab+{b}^{2}\right)[/latex]

7. [latex]\left(10x - 1\right)\left(100{x}^{2}+10x+1\right)[/latex]

8. [latex]{\left(5a - 1\right)}^{-\frac{1}{4}}\left(17a - 2\right)[/latex]

Solutions to Odd-Numbered Exercises

1. The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, [latex]4{x}^{2}[/latex] and [latex]-9{y}^{2}[/latex] don’t have a common factor, but the whole polynomial is still factorable: [latex]4{x}^{2}-9{y}^{2}=\left(2x+3y\right)\left(2x - 3y\right)[/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]10{m}^{3}[/latex]

9. [latex]y[/latex]

11. [latex]\left(2a - 3\right)\left(a+6\right)[/latex]

13. [latex]\left(3n - 11\right)\left(2n+1\right)[/latex]

15. [latex]\left(p+1\right)\left(2p - 7\right)[/latex]

17. [latex]\left(5h+3\right)\left(2h - 3\right)[/latex]

19. [latex]\left(9d - 1\right)\left(d - 8\right)[/latex]

21. [latex]\left(12t+13\right)\left(t - 1\right)[/latex]

23. [latex]\left(4x+10\right)\left(4x - 10\right)[/latex]

25. [latex]\left(11p+13\right)\left(11p - 13\right)[/latex]

27. [latex]\left(19d+9\right)\left(19d - 9\right)[/latex]

29. [latex]\left(12b+5c\right)\left(12b - 5c\right)[/latex]

31. [latex]{\left(7n+12\right)}^{2}[/latex]

33. [latex]{\left(15y+4\right)}^{2}[/latex]

35. [latex]{\left(5p - 12\right)}^{2}[/latex]

37. [latex]\left(x+6\right)\left({x}^{2}-6x+36\right)[/latex]

39. [latex]\left(5a+7\right)\left(25{a}^{2}-35a+49\right)[/latex]

41. [latex]\left(4x - 5\right)\left(16{x}^{2}+20x+25\right)[/latex]

43. [latex]\left(5r+12s\right)\left(25{r}^{2}-60rs+144{s}^{2}\right)[/latex]

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

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

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

51. [latex]\left(14x - 3\right)\left(7x+9\right)[/latex]

53. [latex]\left(3x+5\right)\left(3x - 5\right)[/latex]

55. [latex]{\left(2x+5\right)}^{2}{\left(2x - 5\right)}^{2}[/latex]

57. [latex]\left(4{z}^{2}+49{a}^{2}\right)\left(2z+7a\right)\left(2z - 7a\right)[/latex]

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