6.6 Divide Polynomials

Before you get started, take this readiness quiz.

Add: $\frac{3}{d} + \frac{x}{d} .$
If you missed this problem, review the reference.

Simplify: $\frac{30 x y^{3}}{5 x y} .$
If you missed this problem, review the reference.

Combine like terms: $8 a^{2} + 12 a + 1 + 3 a^{2} - 5 a + 4 .$
If you missed this problem, review the reference.

Find the quotient: $\frac{7 y^{2} + 21}{7} .$

Find the quotient: $\frac{8 z^{2} + 24}{4} .$

Find the quotient: $\frac{18 z^{2} - 27}{9} .$

Find the quotient: $\left(18 x^{3} - 36 x^{2}\right) \div 6 x .$

Find the quotient: $\left(27 b^{3} - 33 b^{2}\right) \div 3 b .$

Find the quotient: $\left(25 y^{3} - 55 y^{2}\right) \div 5 y .$

Find the quotient: $\frac{12 d^{2} - 16 d}{−4} .$

Find the quotient: $\frac{25 y^{2} - 15 y}{−5} .$

Find the quotient: $\frac{42 b^{2} - 18 b}{−6} .$

Find the quotient: $\frac{105 y^{5} + 75 y^{3}}{5 y^{2}} .$

Find the quotient: $\frac{60 d^{7} + 24 d^{5}}{4 d^{3}} .$

Find the quotient: $\frac{216 p^{7} - 48 p^{5}}{6 p^{3}} .$

Find the quotient: $\left(15 x^{3} y - 35 x y^{2}\right) \div \left(−5 x y\right) .$

Find the quotient: $\left(32 a^{2} b - 16 a b^{2}\right) \div \left(−8 a b\right) .$

Find the quotient: $\left(−48 a^{8} b^{4} - 36 a^{6} b^{5}\right) \div \left(−6 a^{3} b^{3}\right) .$

Find the quotient: $\frac{36 x^{3} y^{2} + 27 x^{2} y^{2} - 9 x^{2} y^{3}}{9 x^{2} y} .$

Find the quotient: $\frac{40 x^{3} y^{2} + 24 x^{2} y^{2} - 16 x^{2} y^{3}}{8 x^{2} y} .$

Find the quotient: $\frac{35 a^{4} b^{2} + 14 a^{4} b^{3} - 42 a^{2} b^{4}}{7 a^{2} b^{2}} .$

Find the quotient: $\frac{10 x^{2} + 5 x - 20}{5 x} .$

Find the quotient: $\frac{18 c^{2} + 6 c - 9}{6 c} .$

Find the quotient: $\frac{10 d^{2} - 5 d - 2}{5 d} .$

Find the quotient: $\left(y^{2} + 10 y + 21\right) \div \left(y + 3\right) .$

Find the quotient: $\left(m^{2} + 9 m + 20\right) \div \left(m + 4\right) .$

Find the quotient: $\left(2 x^{2} - 3 x - 20\right) \div \left(x - 4\right) .$

Find the quotient: $\left(3 x^{2} - 16 x - 12\right) \div \left(x - 6\right) .$

Find the quotient: $\left(x^{3} + 5 x^{2} + 8 x + 6\right) \div \left(x + 2\right) .$

Find the quotient: $\left(2 x^{3} + 8 x^{2} + x - 8\right) \div \left(x + 1\right) .$

Find the quotient: $\left(x^{3} + 3 x + 14\right) \div \left(x + 2\right) .$

Find the quotient: $\left(x^{4} - 3 x^{3} - 1000\right) \div \left(x + 5\right) .$

Find the quotient: $\left(x^{3} - 64\right) \div \left(x - 4\right) .$

Find the quotient: $\left(125 x^{3} - 8\right) \div \left(5 x - 2\right) .$

Divide each polynomial by the monomial.

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

Divide each polynomial by the monomial.

$\frac{42 x^{2} - 14 x}{7}$

Divide each polynomial by the monomial.

$\left(55 w^{2} - 10 w\right) \div 5 w$

Divide each polynomial by the monomial.

$\left(8 x^{3} + 6 x^{2}\right) \div 2 x$

Divide each polynomial by the monomial.

$\frac{20 b^{2} - 12 b}{−4}$

Divide each polynomial by the monomial.

$\frac{51 m^{4} + 72 m^{3}}{−3}$

Divide each polynomial by the monomial.

$\frac{412 z^{8} - 48 z^{5}}{4 z^{3}}$

Divide each polynomial by the monomial.

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

Divide each polynomial by the monomial.

$\left(35 x^{4} - 21 x\right) \div \left(−7 x\right)$

Divide each polynomial by the monomial.

$\left(48 y^{4} - 24 y^{3}\right) \div \left(−8 y^{2}\right)$

Divide each polynomial by the monomial.

$\left(45 x^{3} y^{4} + 60 x y^{2}\right) \div \left(5 x y\right)$

Divide each polynomial by the monomial.

$\frac{49 c^{2} d^{2} - 70 c^{3} d^{3} - 35 c^{2} d^{4}}{7 c d^{2}}$

Divide each polynomial by the monomial.

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

Divide each polynomial by the monomial.

$\frac{12 q^{2} + 3 q - 1}{3 q}$

Divide each polynomial by the monomial.

$\frac{20 y^{2} + 12 y - 1}{−4 y}$

Divide each polynomial by the monomial.

$\frac{63 a^{3} - 108 a^{2} + 99 a}{9 a^{2}}$

Divide each polynomial by the binomial.

$\left(d^{2} + 8 d + 12\right) \div \left(d + 2\right)$

Divide each polynomial by the binomial.

$\left(a^{2} - 2 a - 35\right) \div \left(a + 5\right)$

Divide each polynomial by the binomial.

$\left(x^{2} - 14 x + 49\right) \div \left(x - 7\right)$

Divide each polynomial by the binomial.

$\left(4 x^{2} - 17 x - 15\right) \div \left(x - 5\right)$

Divide each polynomial by the binomial.

$\left(p^{2} + 11 p + 16\right) \div \left(p + 8\right)$

Divide each polynomial by the binomial.

$\left(x^{2} + 2 x - 30\right) \div \left(x - 5\right)$

Divide each polynomial by the binomial.

$\left(2 n^{3} - 10 n + 24\right) \div \left(n + 3\right)$

Divide each polynomial by the binomial.

$\left(7 q^{3} - 5 q - 2\right) \div \left(q - 1\right)$

Divide each polynomial by the binomial.

$\left(m^{3} + 1000\right) \div \left(m + 10\right)$

Divide each polynomial by the binomial.

$\left(x^{3} - 216\right) \div \left(x - 6\right)$

Divide each polynomial by the binomial.

$\left(125 y^{3} - 64\right) \div \left(5 y - 4\right)$

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

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