6.6E: Exercises
- Last updated
- Dec 3, 2023
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In the following exercises, divide each polynomial by the monomial.
\dfrac{45y+36}{9}
\dfrac{30b+75}{5}
- Answer
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6b+15
\dfrac{8d^2−4d}{2}
\dfrac{42x^2−14x}{7}
- Answer
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6x^2−2x
(16y^2−20y)÷4y
(55w^2−10w)÷5w
- Answer
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11w−2
(9n^4+6n^3)÷3n
(8x^3+6x^2)÷2x
- Answer
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4x^2+3x
\dfrac{18y^2−12y}{−6}
\dfrac{20b^2−12b}{−4}
- Answer
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−5b^2+3b
\dfrac{35a^4+65a^2}{−5}
\dfrac{51m^4+72m^3}{−3}
- Answer
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−17m^4−24m^3
\dfrac{310y^4−200y^3}{5y^2}
\dfrac{412z^8−48z^5}{4z^3}
- Answer
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103z^5−12z^2
\dfrac{46x^3+38x^2}{2x^2}
\dfrac{51y^4+42y^2}{3y^2}
- Answer
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17y^2+14
(24p^2−33p)÷(−3p)
(35x^4−21x)÷(−7x)
- Answer
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−5x^3+3
(63m^4−42m^3)÷(−7m^2)
(48y^4−24y^3)÷(−8y^2)
- Answer
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−6y^2+3y
(63a^{2}b^3+72ab^4)÷(9ab)
(45x^{3}y^4+60xy^2)÷(5xy)
- Answer
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9x^{2}y^3+12y
\dfrac{52p^{5}q^4+36p^{4}q^3−64p^{3}q^2}{4p^{2}q}
\dfrac{49c^{2}d^2−70c^{3}d^3−35c^{2}d}{7cd^2}
- Answer
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7c−10c^{2}d−\dfrac{5c}{d}
\dfrac{66x^{3}y^2−110x^{2}y^3−44x^{4}y^3}{11x^{2}y^2}
\dfrac{72r^{5}s^2+132r^{4}s^3−96r^{3}s^5}{12r^{2}s^2}
- Answer
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6r^3+11r^{2}s−8rs^3
\dfrac{4w^2+2w−5}{2w}
\dfrac{12q^2+3q−1}{3q}
- Answer
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4q+1−\dfrac{1}{3q}
\dfrac{10x^2+5x−4}{−5x}
\dfrac{20y^2+12y−1}{−4y}
- Answer
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−5y−3+\dfrac{1}{4y}
\dfrac{36p^3+18p^2−12p}{6p^2}
\dfrac{63a^3−108a^2+99a}{9a^2}
- Answer
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7a−12+\dfrac{11}{a}
Divide a Polynomial by a Binomial
In the following exercises, divide each polynomial by the binomial.
(y^2+7y+12)÷(y+3)
(d^2+8d+12)÷(d+2)
- Answer
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d+6
(x^2−3x−10)÷(x+2)
(a^2−2a−35)÷(a+5)
- Answer
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a−7
(t^2−12t+36)÷(t−6)
(x^2−14x+49)÷(x−7)
- Answer
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x−7
(6m^2−19m−20)÷(m−4)
(4x^2−17x−15)÷(x−5)
- Answer
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4x+3
(q^2+2q+20)÷(q+6)
(p^2+11p+16)÷(p+8)
- Answer
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p+3−\dfrac{8}{p+8}
(y^2−3y−15)÷(y−8)
(x^2+2x−30)÷(x−5)
- Answer
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x+7+\dfrac{5}{x−5}
(3b^3+b^2+2)÷(b+1)
(2n^3−10n+28)÷(n+3)
- Answer
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2n^2−6n+8 + \frac{4}{n+3}
(2y^3−6y−36)÷(y−3)
(7q^3−5q−2)÷(q−1)
- Answer
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7q^2+7q+2
(z^3+1)÷(z+1)
(m^3+1000)÷(m+10)
- Answer
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m^2−10m+100
(a^3−125)÷(a−5)
(x^3−216)÷(x−6)
- Answer
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x^2+6x+36
(64x^3−27)÷(4x−3)
(125y^3−64)÷(5y−4)
- Answer
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25y^2+20x+16
Everyday Math
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?
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
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45
Writing Exercises
James divides 48y+6 by 6 this way: \dfrac{48y+6}{6}=48y
Divide \dfrac{10x^2+x−12}{2x} and explain with words how you get each term of the quotient.
- Answer
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Answers will vary.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all goals?
