Instructions: For questions 1-32, divide each polynomial by the monomial.
1. [latex]\frac{45y+36}{9}[/latex]
2. [latex]\frac{30b+75}{5}[/latex]
Solution
[latex]6b+15[/latex]
3. [latex]\frac{8{d}^{2}-4d}{2}[/latex]
4. [latex]\frac{42{x}^{2}-14x}{7}[/latex]
Solution
[latex]6{x}^{2}-2x[/latex]
5. [latex]\left(16{y}^{2}-20y\right)\div 4y[/latex]
6. [latex]\left(55{w}^{2}-10w\right)\div 5w[/latex]
Solution
[latex]11w-2[/latex]
7. [latex]\left(9{n}^{4}+6{n}^{3}\right)\div 3n[/latex]
8. [latex]\left(8{x}^{3}+6{x}^{2}\right)\div 2x[/latex]
Solution
[latex]4{x}^{2}+3x[/latex]
9. [latex]\frac{18{y}^{2}-12y}{-6}[/latex]
10. [latex]\frac{20{b}^{2}-12b}{-4}[/latex]
Solution
[latex]-5{b}^{2}+3b[/latex]
11. [latex]\frac{35{a}^{4}+65{a}^{2}}{-5}[/latex]
12. [latex]\frac{51{m}^{4}+72{m}^{3}}{-3}[/latex]
Solution
[latex]-17{m}^{4}-24{m}^{3}[/latex]
13. [latex]\frac{310{y}^{4}-200{y}^{3}}{5{y}^{2}}[/latex]
14. [latex]\frac{412{z}^{8}-48{z}^{5}}{4{z}^{3}}[/latex]
Solution
[latex]103{z}^{5}-12{z}^{2}[/latex]
15. [latex]\frac{46{x}^{3}+38{x}^{2}}{2{x}^{2}}[/latex]
16. [latex]\frac{51{y}^{4}+42{y}^{2}}{3{y}^{2}}[/latex]
Solution
[latex]17{y}^{2}+14[/latex]
17. [latex]\left(24{p}^{2}-33p\right)\div \left(-3p\right)[/latex]
18. [latex]\left(35{x}^{4}-21x\right)\div \left(-7x\right)[/latex]
Solution
[latex]-5{x}^{3}+3[/latex]
19. [latex]\left(63{m}^{4}-42{m}^{3}\right)\div \left(-7{m}^{2}\right)[/latex]
20. [latex]\left(48{y}^{4}-24{y}^{3}\right)\div \left(-8{y}^{2}\right)[/latex]
Solution
[latex]-6{y}^{2}+3y[/latex]
21. [latex]\left(63{a}^{2}{b}^{3}+72a{b}^{4}\right)\div \left(9ab\right)[/latex]
22. [latex]\left(45{x}^{3}{y}^{4}+60x{y}^{2}\right)\div \left(5xy\right)[/latex]
Solution
[latex]9{x}^{2}{y}^{3}+12y[/latex]
23. [latex]\frac{52{p}^{5}{q}^{4}+36{p}^{4}{q}^{3}-64{p}^{3}{q}^{2}}{4{p}^{2}q}[/latex]
24. [latex]\frac{49{c}^{2}{d}^{2}-70{c}^{3}{d}^{3}-35{c}^{2}{d}^{4}}{7c{d}^{2}}[/latex]
Solution
[latex]7c-10{c}^{2}d-5c{d}^{2}[/latex]
25. [latex]\frac{66{x}^{3}{y}^{2}-110{x}^{2}{y}^{3}-44{x}^{4}{y}^{3}}{11{x}^{2}{y}^{2}}[/latex]
26. [latex]\frac{72{r}^{5}{s}^{2}+132{r}^{4}{s}^{3}-96{r}^{3}{s}^{5}}{12{r}^{2}{s}^{2}}[/latex]
Solution
[latex]6{r}^{3}+11{r}^{2}s-8r{s}^{3}[/latex]
27. [latex]\frac{4{w}^{2}+2w-5}{2w}[/latex]
28. [latex]\frac{12{q}^{2}+3q-1}{3q}[/latex]
Solution
[latex]4q+1-\frac{1}{3q}[/latex]
29. [latex]\frac{10{x}^{2}+5x-4}{-5x}[/latex]
30. [latex]\frac{20{y}^{2}+12y-1}{-4y}[/latex]
Solution
[latex]-5y-3+\frac{1}{4y}[/latex]
31. [latex]\frac{36{p}^{3}+18{p}^{2}-12p}{6{p}^{2}}[/latex]
32. [latex]\frac{63{a}^{3}-108{a}^{2}+99a}{9{a}^{2}}[/latex]
Solution
[latex]7a-12+\frac{11}{a}[/latex]
Instructions: For questions 33-54, divide each polynomial by the binomial.
33. [latex]\left({y}^{2}+7y+12\right)\div \left(y+3\right)[/latex]
34. [latex]\left({d}^{2}+8d+12\right)\div \left(d+2\right)[/latex]
Solution
[latex]d+6[/latex]
35. [latex]\left({x}^{2}-3x-10\right)\div \left(x+2\right)[/latex]
36. [latex]\left({a}^{2}-2a-35\right)\div \left(a+5\right)[/latex]
Solution
[latex]a-7[/latex]
37. [latex]\left({t}^{2}-12t+36\right)\div \left(t-6\right)[/latex]
38. [latex]\left({x}^{2}-14x+49\right)\div \left(x-7\right)[/latex]
Solution
[latex]x-7[/latex]
39. [latex]\left(6{m}^{2}-19m-20\right)\div \left(m-4\right)[/latex]
40. [latex]\left(4{x}^{2}-17x-15\right)\div \left(x-5\right)[/latex]
Solution
[latex]4x+3[/latex]
41. [latex]\left({q}^{2}+2q+20\right)\div \left(q+6\right)[/latex]
42. [latex]\left({p}^{2}+11p+16\right)\div \left(p+8\right)[/latex]
Solution
[latex]p+3-\frac{8}{p+8}[/latex]
43. [latex]\left({y}^{2}-3y-15\right)\div \left(y-8\right)[/latex]
44. [latex]\left({x}^{2}+2x-30\right)\div \left(x-5\right)[/latex]
Solution
[latex]x+7+\frac{5}{x-5}[/latex]
45. [latex]\left(3{b}^{3}+{b}^{2}+2\right)\div \left(b+1\right)[/latex]
46. [latex]\left(2{n}^{3}-10n+24\right)\div \left(n+3\right)[/latex]
Solution
[latex]2{n}^{2}-6n+8[/latex]
47. [latex]\left(2{y}^{3}-6y-36\right)\div \left(y-3\right)[/latex]
48. [latex]\left(7{q}^{3}-5q-2\right)\div \left(q-1\right)[/latex]
Solution
[latex]7{q}^{2}+7q+2[/latex]
49. [latex]\left({z}^{3}+1\right)\div \left(z+1\right)[/latex]
50. [latex]\left({m}^{3}+1000\right)\div \left(m+10\right)[/latex]
Solution
[latex]{m}^{2}-10m+100[/latex]
51. [latex]\left({a}^{3}-125\right)\div \left(a-5\right)[/latex]
52. [latex]\left({x}^{3}-216\right)\div \left(x-6\right)[/latex]
Solution
[latex]{x}^{2}+6x+36[/latex]
53. [latex]\left(64{x}^{3}-27\right)\div \left(4x-3\right)[/latex]
54. [latex]\left(125{y}^{3}-64\right)\div \left(5y-4\right)[/latex]
Solution
[latex]25{y}^{2}+20x+16[/latex]
