Chapter 5

Multiply. \(\left(-5.2 x^{4}\right)\left(3 x^{4}\right)\)

$$ \left(1.2 x^{3}-3.4 x+7.9\right)+\left(6.7 x^{3}+4.4 x^{2}-10.9\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{-9 x^{5}+3 x^{4}-12}{3 x^{3}} $$

Find the degree of each polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. See Examples 2 and 3. $$ 12 x^{4}-x^{6}-12 x^{2} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{1}{p^{-3}} $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (2 x+5)(3 x-1) $$

Evaluate each expression. $$ \left(\frac{1}{3}\right)^{3} $$

Multiply. \(\left(-\frac{1}{3} y^{2}\right)\left(\frac{2}{5} y\right)\)

$$ \left(9.6 y^{3}+2.7 y^{2}-8.6\right)+\left(1.1 y^{3}-8.8 y+11.6\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{6 a^{2}-4 a+12}{-2 a^{2}} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{1}{q^{-5}} $$

Evaluate each expression. $$ \left(-\frac{1}{9}\right)^{2} $$

Multiply. \(\left(-\frac{3}{4} y^{7}\right)\left(\frac{1}{7} y^{4}\right)\)

$$ \left(\frac{3}{4} m^{2}-\frac{2}{5} m+\frac{1}{8}\right)+\left(-\frac{1}{4} m^{2}-\frac{3}{10} m+\frac{11}{16}\right) $$

Find the degree of each polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. See Examples 2 and 3. $$ 3 z-5 z^{4} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{p^{-5}}{q^{-4}} $$

Evaluate each expression. $$ 7 \cdot 2^{4} $$

Multiply. \((2 x)\left(-3 x^{2}\right)\left(4 x^{5}\right)\)

$$ \left(-\frac{4}{7} n^{2}+\frac{5}{6} m-\frac{1}{20}\right)+\left(\frac{3}{7} n^{2}-\frac{5}{12} m-\frac{3}{10}\right) $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{r^{-5}}{s^{-2}} $$

Multiply using the FOIL method. See Examples 1 through 3. $$ \left(y^{2}+3\right)(5 y+6) $$

Evaluate each expression. $$ 9 \cdot 2^{2} $$

Multiply. \((x)\left(5 x^{4}\right)\left(-6 x^{7}\right)\)

Add using a vertical format. $$ \begin{array}{l} 3 t^{2}+4 \\ 5 t^{2}-8 \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{x^{-2}}{x} $$

Evaluate each expression with the given replacement values. $$ x^{2} \text { when } x=-2 $$

Multiply using the FOIL method. See Examples 1 through 3. $$ \left(x-\frac{1}{3}\right)\left(x+\frac{2}{3}\right) $$

Multiply. \(3 x(2 x+5)\)

Add using a vertical format. $$ \begin{array}{l} 7 x^{3}+3 \\ 2 x^{3}-7 \\ \hline \end{array} $$

Evaluate each polynomial when (a) \(x=0\) and \((b) x=-1 .\) See Examples 4 and 5. $$ 2 x-10 $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{y}{y^{-3}} $$

Evaluate each expression with the given replacement values. $$ x^{3} \text { when } x=-2 $$

Multiply using the FOIL method. See Examples 1 through 3. $$ \left(x-\frac{2}{5}\right)\left(x+\frac{1}{5}\right) $$

Multiply. \(2 x(6 x+3)\)

Add using a vertical format. $$ \begin{array}{r} 10 a^{3}-8 a^{2}+4 a+9 \\ 5 a^{3}+9 a^{2}-7 a+7 \end{array} $$

Evaluate each polynomial when (a) \(x=0\) and \((b) x=-1 .\) See Examples 4 and 5. $$ x^{2}-5 x-2 $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{z^{-4}}{z^{-7}} $$

Evaluate each expression with the given replacement values. $$ 5 x^{3} \text { when } x=3 $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (0.4-3 a)(0.2-5 a) $$

Multiply. \(7 x\left(x^{2}+2 x-1\right)\)

Add using a vertical format. $$ \begin{array}{l} 2 x^{3}-3 x^{2}+x-4 \\ 5 x^{3}+2 x^{2}-3 x+2 \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ \frac{x^{-4}}{x^{-1}} $$

Evaluate each expression with the given replacement values. $$ 4 x^{2} \text { when } x=5 $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (0.3-2 a)(0.6-5 a) $$

Multiply. \(5 y\left(y^{2}+y-10\right)\)

Subtract $$ (2 x+5)-(3 x-9) $$

Evaluate each polynomial when (a) \(x=0\) and \((b) x=-1 .\) See Examples 4 and 5. $$ -x^{3}+4 x^{2}-15 $$

Simplify each expression. Write each result using positive exponents only. $$ 3^{-2}+3^{-1} $$

Evaluate each expression with the given replacement values. $$ 2 x y^{2} \text { when } x=3 \text { and } y=-5 $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (x+5 y)(2 x-y) $$