Chapter 6

Label the dividend, divisor, and quotient of each division problem. $$\frac{12 c^{3}+20 c^{2}-4 c}{4 c}=3 c^{2}+5 c-1$$

Explain how to multiply two monomials.

Is the given expression a polynomial? Why or why not? $$-5 z^{2}-4 z+12$$

Evaluate using the rules of exponents. $$2^{2} \cdot 2^{4}$$

Label the dividend, divisor, and quotient of each division problem. $$2 p + 3 \longdiv { 1 0 p ^ { 3 } + p ^ { 2 } - 2 5 p - 6 } ^ { 5 p ^ { 2 } - 7 p - 2 }$$

Explain how to multiply a monomial by a trinomial.

Is the given expression a polynomial? Why or why not? $$9 t^{3}+t^{2}-t+\frac{3}{8}$$

Evaluate using the rules of exponents. $$(-3)^{2} \cdot(-3)$$

Explain, in your own words, how to divide a polynomial by a monomial.

Multiply. $$\left(7 k^{4}\right)\left(2 k^{2}\right)$$

Evaluate using the rules of exponents. $$\frac{(-4)^{8}}{(-4)^{5}}$$

When do you use long division to divide polynomials?

Multiply. $$\left(3 z^{7}\right)\left(5 z^{3}\right)$$

Is the given expression a polynomial? Why or why not? $$6 y^{4}$$

Evaluate using the rules of exponents. $$\frac{2^{10}}{2^{6}}$$

Divide. $$\frac{4 a^{5}-10 a^{4}+6 a^{3}}{2 a^{3}}$$

Multiply. $$(-4 t)\left(6 t^{8}\right)$$

Evaluate using the rules of exponents. $$6^{-1}$$

Is the given expression a polynomial? Why or why not? $$8 c-5+\frac{2}{c}$$

Divide. $$\frac{28 k^{4}+8 k^{3}-40 k^{2}}{4 k^{2}}$$

Multiply. $$\left(8 p^{6}\right)\left(-p^{4}\right)$$

Evaluate using the rules of exponents. $$(12)^{-2}$$

Divide. $$\frac{18 u^{7}+18 u^{5}+45 u^{4}-72 u^{2}}{9 u^{2}}$$

Multiply. $$\left(\frac{7}{10} d^{9}\right)\left(\frac{5}{2} d^{2}\right)$$

Determine whether each is a monomial, a binomial, or a trinomial. $$3 x-7$$

Evaluate using the rules of exponents. $$\left(\frac{1}{9}\right)^{-2}$$

Divide. $$\frac{-15 m^{6}+10 m^{5}+20 m^{4}-35 m^{3}}{5 m^{3}}$$

Multiply. $$\left(-\frac{8}{9} c^{5}\right)\left(\frac{3}{10} c^{7}\right)$$

Determine whether each is a monomial, a binomial, or a trinomial. $$-w^{3}$$

Evaluate using the rules of exponents. $$\left(-\frac{1}{5}\right)^{-3}$$

Divide. $$\left(35 d^{5}-7 d^{2}\right) \div\left(-7 d^{2}\right)$$

Multiply. $$7 y(4 y-9)$$

Determine whether each is a monomial, a binomial, or a trinomial. $$a^{2} b^{2}+10 a b-6$$

Evaluate using the rules of exponents. $$\left(\frac{3}{2}\right)^{-4}$$

Divide. $$\left(-32 q^{6}-8 q^{3}+4 q^{2}\right) \div\left(-4 q^{2}\right)$$

Determine whether each is a monomial, a binomial, or a trinomial. $$16 r^{2}+9 r$$

Evaluate using the rules of exponents. $$\left(\frac{7}{9}\right)^{-2}$$

Divide. $$\frac{9 w^{5}+42 w^{4}-6 w^{3}+3 w^{2}}{6 w^{3}}$$

Multiply. $$-4 b(9 b+8)$$

Evaluate using the rules of exponents. $$6^{0}+\left(-\frac{1}{2}\right)^{-5}$$

Divide. $$\frac{-54 j^{5}+30 j^{3}-9 j^{2}+15}{9 j}$$

Multiply. $$-12 m(11 m-4)$$

Determine whether each is a monomial, a binomial, or a trinomial. $$v^{4}+7 v^{2}+6$$

Evaluate using the rules of exponents. $$\left(\frac{1}{4}\right)^{-2}+\left(\frac{1}{4}\right)^{0}$$

Divide. $$\left(10 v^{7}-36 v^{5}-22 v^{4}-5 v^{2}+1\right) \div\left(4 v^{4}\right)$$

Multiply. $$6 v^{3}\left(v^{2}-4 v-2\right)$$

How do you determine the degree of a polynomial in one variable?

Evaluate using the rules of exponents. $$\frac{8^{5}}{8^{7}}$$

Divide. $$\left(60 z^{5}+3 z^{4}-10 z\right) \div\left(5 z^{2}\right)$$

Multiply. $$3 x^{4}\left(5 x^{3}+x-7\right)$$