6.6E: Exercises
- Page ID
- 30256
Practice Makes Perfect
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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\(9x^{2}y^3+12y\)
\(\dfrac{52p^{5}q^4+36p^{4}q^3−64p^{3}q^2}{4p^{2}q}\)
\(\dfrac{49c^{2}d^2−70c^{3}d^3−35c^{2}d}{47cd^2}\)
- Answer
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\(7c−10c^{2}d−5cd^2\)
\(\dfrac{66x^{3}y^2−110x^{2}y^3−44x^{4}y^3}{11x^{2}y^2}\)
\(\dfrac{72r^{5}s^2+132r^{4}s^3−96r^{3}s^5}{12r^{2}s^2}\)
- 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?