1. No, a quotient of polynomials can only be decomposed if the denominator can be factored. For example, x2+11 cannot be decomposed because the denominator cannot be factored.
3. Graph both sides and ensure they are equal.
5. If we choose x=−1, then the B-term disappears, letting us immediately know that A=3. We could alternatively plug in x=−35, giving us a B-value of −2.
7. x+38−x−85
9. x+51+x+29
11. 5x−23+4x−14
13. 2(x+3)5+2(x−3)5
15. x+23+x−23
17. 5(x+2)9+5(x−3)11
19. x−38−x−25
21. x−21+(x−2)22
23. −4x+56+(4x+5)23
25. −x−71−(x−7)22
27. x4−2(x+1)3+2(x+1)27
29. x4+x22−3x+23+2(3x+2)27
31. x2+x+3x+1+x+23
33. x2+3x+84−3x+x−11
35. x2+6x+12x−1+x+32
37. x2+x+11+x−14
39. x2−3x+92+x+33
41. −4x2+6x+91+2x−31
43. x1+x+61−x2−6x+364x
45. x2+1x+6+(x2+1)24x+3
47. x+2x+1+(x+2)22x+3
49. x2+3x+251−(x2+3x+25)23x
51. 8x1−8(x2+4)x+2(x2+4)210−x
53. −x16−x29+x−116−(x−1)27
55. x+11−(x+1)22+(x+1)35
57. x−25−10(x+2)3+x+87−10(x−8)7
59. −4x5−2(x+2)5+2(x+4)11+4(x+4)5