6.6E: Exercises

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Lynn Marecek
Professor (Mathematics) at Santa Ana College
Publisher: OpenStax CNX

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Practice Makes Perfect

In the following exercises, divide each polynomial by the monomial.

Exercise 1

$\dfrac{45y+36}{9}$

Exercise 2

$\dfrac{30b+75}{5}$

Answer: $6b+15$

Exercise 3

$\dfrac{8d^2−4d}{2}$

Exercise 4

$\dfrac{42x^2−14x}{7}$

Answer: $6x^2−2x$

Exercise 5

$(16y^2−20y)÷4y$

Exercise 6

$(55w^2−10w)÷5w$

Answer: $11w−2$

Exercise 7

$(9n^4+6n^3)÷3n$

Exercise 8

$(8x^3+6x^2)÷2x$

Answer: $4x^2+3x$

Exercise 9

$\dfrac{18y^2−12y}{−6}$

Exercise 10

$\dfrac{20b^2−12b}{−4}$

Answer: $−5b^2+3b$

Exercise 11

$\dfrac{35a^4+65a^2}{−5}$

Exercise 12

$\dfrac{51m^4+72m^3}{−3}$

Answer: $−17m^4−24m^3$

Exercise 13

$\dfrac{310y^4−200y^3}{5y^2}$

Exercise 14

$\dfrac{412z^8−48z^5}{4z^3}$

Answer: $103z^5−12z^2$

Exercise 15

$\dfrac{46x^3+38x^2}{2x^2}$

Exercise 16

$\dfrac{51y^4+42y^2}{3y^2}$

Answer: $17y^2+14$

Exercise 17

$(24p^2−33p)÷(−3p)$

Exercise 18

$(35x^4−21x)÷(−7x)$

Answer: $−5x^3+3$

Exercise 19

$(63m^4−42m^3)÷(−7m^2)$

Exercise 20

$(48y^4−24y^3)÷(−8y^2)$

Answer: $−6y^2+3y$

Exercise 21

$(63a^{2}b^3+72ab^4)÷(9ab)$

Exercise 22

$(45x^{3}y^4+60xy^2)÷(5xy)$

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

Exercise 23

$\dfrac{52p^{5}q^4+36p^{4}q^3−64p^{3}q^2}{4p^{2}q}$

Exercise 24

$\dfrac{49c^{2}d^2−70c^{3}d^3−35c^{2}d}{47cd^2}$

Answer: $7c−10c^{2}d−5cd^2$

Exercise 25

$\dfrac{66x^{3}y^2−110x^{2}y^3−44x^{4}y^3}{11x^{2}y^2}$

Exercise 26

$\dfrac{72r^{5}s^2+132r^{4}s^3−96r^{3}s^5}{12r^{2}s^2}$

Answer: $6r^3+11r^{2}s−8rs^3$

Exercise 27

$\dfrac{4w^2+2w−5}{2w}$

Exercise 28

$\dfrac{12q^2+3q−1}{3q}$

Answer: $4q+1−\dfrac{1}{3q}$

Exercise 29

$\dfrac{10x^2+5x−4}{−5x}$

Exercise 30

$\dfrac{20y^2+12y−1}{−4y}$

Answer: $−5y−3+\dfrac{1}{4y}$

Exercise 31

$\dfrac{36p^3+18p^2−12p}{6p^2}$

Exercise 32

$\dfrac{63a^3−108a^2+99a}{9a^2}$

Answer: $7a−12+\dfrac{11}{a}$

Divide a Polynomial by a Binomial

In the following exercises, divide each polynomial by the binomial.

Exercise 33

$(y^2+7y+12)÷(y+3)$

Exercise 34

$(d^2+8d+12)÷(d+2)$

Answer: $d+6$

Exercise 35

$(x^2−3x−10)÷(x+2)$

Exercise 36

$(a^2−2a−35)÷(a+5)$

Answer: $a−7$

Exercise 37

$(t^2−12t+36)÷(t−6)$

Exercise 38

$(x^2−14x+49)÷(x−7)$

Answer: $x−7$

Exercise 39

$(6m^2−19m−20)÷(m−4)$

Exercise 40

$(4x^2−17x−15)÷(x−5)$

Answer: $4x+3$

Exercise 41

$(q^2+2q+20)÷(q+6)$

Exercise 42

$(p^2+11p+16)÷(p+8)$

Answer: $p+3−\dfrac{8}{p+8}$

Exercise 43

$(y^2−3y−15)÷(y−8)$

Exercise 44

$(x^2+2x−30)÷(x−5)$

Answer: $x+7+\dfrac{5}{x−5}$

Exercise 45

$(3b^3+b^2+2)÷(b+1)$

Exercise 46

$(2n^3−10n+28)÷(n+3)$

Answer: $2n^2−6n+8 + \frac{4}{n+3}$

Exercise 47

$(2y^3−6y−36)÷(y−3)$

Exercise 48

$(7q^3−5q−2)÷(q−1)$

Answer: $7q^2+7q+2$

Exercise 49

$(z^3+1)÷(z+1)$

Exercise 50

$(m^3+1000)÷(m+10)$

Answer: $m^2−10m+100$

Exercise 51

$(a^3−125)÷(a−5)$

Exercise 52

$(x^3−216)÷(x−6)$

Answer: $x^2+6x+36$

Exercise 53

$(64x^3−27)÷(4x−3)$

Exercise 54

$(125y^3−64)÷(5y−4)$

Answer: $25y^2+20x+16$

Everyday Math

Exercise 55

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

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

Exercise 56

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

Answer: 45

Writing Exercises

Exercise 57

James divides $48y+6$ by $6$ this way: $\dfrac{48y+6}{6}=48y$

Exercise 58

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

Answer: Answers will vary.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

$This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “divide a polynomial by a monomial,” and “divide a polynomial by a binomial.” The rest of the cells are blank.$

ⓑ After reviewing this checklist, what will you do to become confident for all goals?