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Mathematics LibreTexts

6.6E: Exercises

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    30544
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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 \(\dfrac{7x+500}{x}\)

    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?

    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?

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