# Exercises: Divide Polynomials (5.6)

## Exercises: Divide a Polynomial by a Monomial

Instructions: For questions 1-32, divide each polynomial by the monomial.
1. $\frac{45y+36}{9}$

2. $\frac{30b+75}{5}$
Solution

$6b+15$

3. $\frac{8{d}^{2}-4d}{2}$

4. $\frac{42{x}^{2}-14x}{7}$
Solution

$6{x}^{2}-2x$

5. $\left(16{y}^{2}-20y\right)\div 4y$

6. $\left(55{w}^{2}-10w\right)\div 5w$
Solution

$11w-2$

7. $\left(9{n}^{4}+6{n}^{3}\right)\div 3n$

8. $\left(8{x}^{3}+6{x}^{2}\right)\div 2x$
Solution

$4{x}^{2}+3x$

9. $\frac{18{y}^{2}-12y}{-6}$

10. $\frac{20{b}^{2}-12b}{-4}$
Solution

$-5{b}^{2}+3b$

11. $\frac{35{a}^{4}+65{a}^{2}}{-5}$

12. $\frac{51{m}^{4}+72{m}^{3}}{-3}$
Solution

$-17{m}^{4}-24{m}^{3}$

13. $\frac{310{y}^{4}-200{y}^{3}}{5{y}^{2}}$

14. $\frac{412{z}^{8}-48{z}^{5}}{4{z}^{3}}$
Solution

$103{z}^{5}-12{z}^{2}$

15. $\frac{46{x}^{3}+38{x}^{2}}{2{x}^{2}}$

16. $\frac{51{y}^{4}+42{y}^{2}}{3{y}^{2}}$
Solution

$17{y}^{2}+14$

17. $\left(24{p}^{2}-33p\right)\div \left(-3p\right)$

18. $\left(35{x}^{4}-21x\right)\div \left(-7x\right)$
Solution

$-5{x}^{3}+3$

19. $\left(63{m}^{4}-42{m}^{3}\right)\div \left(-7{m}^{2}\right)$

20. $\left(48{y}^{4}-24{y}^{3}\right)\div \left(-8{y}^{2}\right)$
Solution

$-6{y}^{2}+3y$

21. $\left(63{a}^{2}{b}^{3}+72a{b}^{4}\right)\div \left(9ab\right)$

22. $\left(45{x}^{3}{y}^{4}+60x{y}^{2}\right)\div \left(5xy\right)$
Solution

$9{x}^{2}{y}^{3}+12y$

23. $\frac{52{p}^{5}{q}^{4}+36{p}^{4}{q}^{3}-64{p}^{3}{q}^{2}}{4{p}^{2}q}$

24. $\frac{49{c}^{2}{d}^{2}-70{c}^{3}{d}^{3}-35{c}^{2}{d}^{4}}{7c{d}^{2}}$
Solution

$7c-10{c}^{2}d-5c{d}^{2}$

25. $\frac{66{x}^{3}{y}^{2}-110{x}^{2}{y}^{3}-44{x}^{4}{y}^{3}}{11{x}^{2}{y}^{2}}$

26. $\frac{72{r}^{5}{s}^{2}+132{r}^{4}{s}^{3}-96{r}^{3}{s}^{5}}{12{r}^{2}{s}^{2}}$
Solution

$6{r}^{3}+11{r}^{2}s-8r{s}^{3}$

27. $\frac{4{w}^{2}+2w-5}{2w}$

28. $\frac{12{q}^{2}+3q-1}{3q}$
Solution

$4q+1-\frac{1}{3q}$

29. $\frac{10{x}^{2}+5x-4}{-5x}$

30. $\frac{20{y}^{2}+12y-1}{-4y}$
Solution

$-5y-3+\frac{1}{4y}$

31. $\frac{36{p}^{3}+18{p}^{2}-12p}{6{p}^{2}}$

32. $\frac{63{a}^{3}-108{a}^{2}+99a}{9{a}^{2}}$
Solution

$7a-12+\frac{11}{a}$

## Exercises: Divide a Polynomial by a Binomial

Instructions: For questions 33-54, divide each polynomial by the binomial.

33. $\left({y}^{2}+7y+12\right)\div \left(y+3\right)$

34. $\left({d}^{2}+8d+12\right)\div \left(d+2\right)$
Solution

$d+6$

35. $\left({x}^{2}-3x-10\right)\div \left(x+2\right)$

36. $\left({a}^{2}-2a-35\right)\div \left(a+5\right)$
Solution

$a-7$

37. $\left({t}^{2}-12t+36\right)\div \left(t-6\right)$

38. $\left({x}^{2}-14x+49\right)\div \left(x-7\right)$
Solution

$x-7$

39. $\left(6{m}^{2}-19m-20\right)\div \left(m-4\right)$

40. $\left(4{x}^{2}-17x-15\right)\div \left(x-5\right)$
Solution

$4x+3$

41. $\left({q}^{2}+2q+20\right)\div \left(q+6\right)$

42. $\left({p}^{2}+11p+16\right)\div \left(p+8\right)$
Solution

$p+3-\frac{8}{p+8}$

43. $\left({y}^{2}-3y-15\right)\div \left(y-8\right)$

44. $\left({x}^{2}+2x-30\right)\div \left(x-5\right)$
Solution

$x+7+\frac{5}{x-5}$

45. $\left(3{b}^{3}+{b}^{2}+2\right)\div \left(b+1\right)$

46. $\left(2{n}^{3}-10n+24\right)\div \left(n+3\right)$
Solution

$2{n}^{2}-6n+8$

47. $\left(2{y}^{3}-6y-36\right)\div \left(y-3\right)$

48. $\left(7{q}^{3}-5q-2\right)\div \left(q-1\right)$
Solution

$7{q}^{2}+7q+2$

49. $\left({z}^{3}+1\right)\div \left(z+1\right)$

50. $\left({m}^{3}+1000\right)\div \left(m+10\right)$
Solution

${m}^{2}-10m+100$

51. $\left({a}^{3}-125\right)\div \left(a-5\right)$

52. $\left({x}^{3}-216\right)\div \left(x-6\right)$
Solution

${x}^{2}+6x+36$

53. $\left(64{x}^{3}-27\right)\div \left(4x-3\right)$

54. $\left(125{y}^{3}-64\right)\div \left(5y-4\right)$
Solution

$25{y}^{2}+20x+16$

## Exercises: Everyday Math

Instructions: For questions 55-56, answer the given everyday math word problems.

55. Average cost. Pictures Plus produces digital albums. The company’s average cost (in dollars) to make $x$ albums is given by the expression $\frac{7x+500}{x}$.

a. Find the quotient by dividing the numerator by the denominator.
b. What will the average cost (in dollars) be to produce $20$ albums?

56. Handshakes. At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression $\frac{{n}^{2}-n}{2}$, where $n$ represents the number of employees. How many handshakes will there be if there are $10$ employees at the meeting?
Solution

$45$

## Exercises: Writing Exercises

Instructions: For questions 57-58, answer the given writing exercises.
57. James divides $48y+6$ by 6 this way: $\frac{48y+\cancel{6}}{\cancel{6}}=48y$. What is wrong with his reasoning?

58. Divide $\frac{10{x}^{2}+x-12}{2x}$ and explain with words how you get each term of the quotient.
Solution

Answers will vary.

## License

Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.