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Solutions

Solutions to Try Its

1. (b2a)(x+6)\left({b}^{2}-a\right)\left(x+6\right) 2. (x6)(x1)\left(x - 6\right)\left(x - 1\right) 3. a. (2x+3)(x+3)\left(2x+3\right)\left(x+3\right) b. (3x1)(2x+1)\left(3x - 1\right)\left(2x+1\right) 4. (7x1)2{\left(7x - 1\right)}^{2} 5. (9y+10)(9y10)\left(9y+10\right)\left(9y - 10\right) 6. (6a+b)(36a26ab+b2)\left(6a+b\right)\left(36{a}^{2}-6ab+{b}^{2}\right) 7. (10x1)(100x2+10x+1)\left(10x - 1\right)\left(100{x}^{2}+10x+1\right) 8. (5a1)14(17a2){\left(5a - 1\right)}^{-\frac{1}{4}}\left(17a - 2\right)

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, 4x24{x}^{2} and 9y2-9{y}^{2} don’t have a common factor, but the whole polynomial is still factorable: 4x29y2=(2x+3y)(2x3y)4{x}^{2}-9{y}^{2}=\left(2x+3y\right)\left(2x - 3y\right). 3. Divide the xx 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. 7m7m 7. 10m310{m}^{3} 9. yy 11. (2a3)(a+6)\left(2a - 3\right)\left(a+6\right) 13. (3n11)(2n+1)\left(3n - 11\right)\left(2n+1\right) 15. (p+1)(2p7)\left(p+1\right)\left(2p - 7\right) 17. (5h+3)(2h3)\left(5h+3\right)\left(2h - 3\right) 19. (9d1)(d8)\left(9d - 1\right)\left(d - 8\right) 21. (12t+13)(t1)\left(12t+13\right)\left(t - 1\right) 23. (4x+10)(4x10)\left(4x+10\right)\left(4x - 10\right) 25. (11p+13)(11p13)\left(11p+13\right)\left(11p - 13\right) 27. (19d+9)(19d9)\left(19d+9\right)\left(19d - 9\right) 29. (12b+5c)(12b5c)\left(12b+5c\right)\left(12b - 5c\right) 31. (7n+12)2{\left(7n+12\right)}^{2} 33. (15y+4)2{\left(15y+4\right)}^{2} 35. (5p12)2{\left(5p - 12\right)}^{2} 37. (x+6)(x26x+36)\left(x+6\right)\left({x}^{2}-6x+36\right) 39. (5a+7)(25a235a+49)\left(5a+7\right)\left(25{a}^{2}-35a+49\right) 41. (4x5)(16x2+20x+25)\left(4x - 5\right)\left(16{x}^{2}+20x+25\right) 43. (5r+12s)(25r260rs+144s2)\left(5r+12s\right)\left(25{r}^{2}-60rs+144{s}^{2}\right) 45. (2c+3)14(7c15){\left(2c+3\right)}^{-\frac{1}{4}}\left(-7c - 15\right) 47. (x+2)25(19x+10){\left(x+2\right)}^{-\frac{2}{5}}\left(19x+10\right) 49. (2z9)32(27z99){\left(2z - 9\right)}^{-\frac{3}{2}}\left(27z - 99\right) 51. (14x3)(7x+9)\left(14x - 3\right)\left(7x+9\right) 53. (3x+5)(3x5)\left(3x+5\right)\left(3x - 5\right) 55. (2x+5)2(2x5)2{\left(2x+5\right)}^{2}{\left(2x - 5\right)}^{2} 57. (4z2+49a2)(2z+7a)(2z7a)\left(4{z}^{2}+49{a}^{2}\right)\left(2z+7a\right)\left(2z - 7a\right) 59. 1(4x+9)(4x9)(2x+3)\frac{1}{\left(4x+9\right)\left(4x - 9\right)\left(2x+3\right)}

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  • College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface. License: CC BY: Attribution.