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6.6E: Exercises

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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

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

$$6b+15$$

Exercise 3

$$\dfrac{8d^2−4d}{2}$$

Exercise 4

$$\dfrac{42x^2−14x}{7}$$

$$6x^2−2x$$

Exercise 5

$$(16y^2−20y)÷4y$$

Exercise 6

$$(55w^2−10w)÷5w$$

$$11w−2$$

Exercise 7

$$(9n^4+6n^3)÷3n$$

Exercise 8

$$(8x^3+6x^2)÷2x$$

$$4x^2+3x$$

Exercise 9

$$\dfrac{18y^2−12y}{−6}$$

Exercise 10

$$\dfrac{20b^2−12b}{−4}$$

$$−5b^2+3b$$

Exercise 11

$$\dfrac{35a^4+65a^2}{−5}$$

Exercise 12

$$\dfrac{51m^4+72m^3}{−3}$$

$$−17m^4−24m^3$$

Exercise 13

$$\dfrac{310y^4−200y^3}{5y^2}$$

Exercise 14

$$\dfrac{412z^8−48z^5}{4z^3}$$

$$103z^5−12z^2$$

Exercise 15

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

Exercise 16

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

$$17y^2+14$$

Exercise 17

$$(24p^2−33p)÷(−3p)$$

Exercise 18

$$(35x^4−21x)÷(−7x)$$

$$−5x^3+3$$

Exercise 19

$$(63m^4−42m^3)÷(−7m^2)$$

Exercise 20

$$(48y^4−24y^3)÷(−8y^2)$$

$$−6y^2+3y$$

Exercise 21

$$(63a^{2}b^3+72ab^4)÷(9ab)$$

Exercise 22

$$(45x^{3}y^4+60xy^2)÷(5xy)$$

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

Exercise 23

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

Exercise 24

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

$$7c−10c^{2}d−5cd^2$$

Exercise 25

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

Exercise 26

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

$$6r^3+11r^{2}s−8rs^3$$

Exercise 27

$$\dfrac{4w^2+2w−5}{2w}$$

Exercise 28

$$\dfrac{12q^2+3q−1}{3q}$$

$$4q+1−\dfrac{1}{3q}$$

Exercise 29

$$\dfrac{10x^2+5x−4}{−5x}$$

Exercise 30

$$\dfrac{20y^2+12y−1}{−4y}$$

$$−5y−3+\dfrac{1}{4y}$$

Exercise 31

$$\dfrac{36p^3+18p^2−12p}{6p^2}$$

Exercise 32

$$\dfrac{63a^3−108a^2+99a}{9a^2}$$

$$7a−12+\dfrac{11}{a}$$

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

$$(d^2+8d+12)÷(d+2)$$

$$d+6$$

Exercise 35

$$(x^2−3x−10)÷(x+2)$$

Exercise 36

$$(a^2−2a−35)÷(a+5)$$

$$a−7$$

Exercise 37

$$(t^2−12t+36)÷(t−6)$$

Exercise 38

$$(x^2−14x+49)÷(x−7)$$

$$x−7$$

Exercise 39

$$(6m^2−19m−20)÷(m−4)$$

Exercise 40

$$(4x^2−17x−15)÷(x−5)$$

$$4x+3$$

Exercise 41

$$(q^2+2q+20)÷(q+6)$$

Exercise 42

$$(p^2+11p+16)÷(p+8)$$

$$p+3−\dfrac{8}{p+8}$$

Exercise 43

$$(y^2−3y−15)÷(y−8)$$

Exercise 44

$$(x^2+2x−30)÷(x−5)$$

$$x+7+\dfrac{5}{x−5}$$

Exercise 45

$$(3b^3+b^2+2)÷(b+1)$$

Exercise 46

$$(2n^3−10n+28)÷(n+3)$$

$$2n^2−6n+8 + \frac{4}{n+3}$$

Exercise 47

$$(2y^3−6y−36)÷(y−3)$$

Exercise 48

$$(7q^3−5q−2)÷(q−1)$$

$$7q^2+7q+2$$

Exercise 49

$$(z^3+1)÷(z+1)$$

Exercise 50

$$(m^3+1000)÷(m+10)$$

$$m^2−10m+100$$

Exercise 51

$$(a^3−125)÷(a−5)$$

Exercise 52

$$(x^3−216)÷(x−6)$$

$$x^2+6x+36$$

Exercise 53

$$(64x^3−27)÷(4x−3)$$

Exercise 54

$$(125y^3−64)÷(5y−4)$$

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

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 $$\dfrac{7x+500}{x}$$

1. Find the quotient by dividing the numerator by the denominator.
2. 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?

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.