Chapter 5

$$ (3 x+7)+(9 x+5) $$

Complete each table for each polynomial. See Example 1. $$ x^{2}-3 x+5 $$ $$ \begin{array}{|c|c|} \hline \text { Term } & \text { Coefficient } \\ \hline x^{2} & \\ \hline & -3 \\ \hline 5 & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ 4^{-3} $$

Evaluate each expression. $$ 7^{2} $$

Multiply. \(8 x^{2} \cdot 3 x\)

Below are some interesting facts about selected countries' national debts during a certain time period. If a number is written in standard form, write it in scientific notation. If a number is written in scientific notation, write it in standard form. (Source: CIA World Factbook). The amount by which Russia's debt is greater than Mexico's debt is \(\$ 24,000,000,000\).

$$ (-y-2)+(3 y+5) $$

Perform each division. See Examples 1 through 3. $$ \frac{20 x^{3}-30 x^{2}+5 x+5}{5} $$

Complete each table for each polynomial. See Example 1. $$ 2 x^{3}-x+4 $$ $$ \begin{array}{|r|c|} \hline \text { Term } & \text { Coefficient } \\ \hline & 2 \\ \hline-x & \\ \hline 4 & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ 6^{-2} $$

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

Evaluate each expression. $$ -3^{2} $$

Multiply. \(6 x \cdot 3 x^{2}\)

$$ (-7 x+5)+\left(-3 x^{2}+7 x+5\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{8 x^{3}-4 x^{2}+6 x+2}{2} $$

Complete each table for each polynomial. See Example 1. $$ -5 x^{4}+3.2 x^{2}+x-5 $$ $$ \begin{array}{|r|r|} \hline \text { Term } & \text { Coefficient } \\ \hline-5 x^{4} & \\ \hline 3.2 x^{2} & \\ \hline x & \\ \hline-5 & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ 7 x^{-3} $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (x-5)(x+10) $$

Evaluate each expression. $$ (-5)^{1} $$

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

$$ (3 x-8)+\left(4 x^{2}-3 x+3\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{15 p^{3}+18 p^{2}}{3 p} $$

Complete each table for each polynomial. See Example 1. $$ 9.7 x^{7}-3 x^{5}+x^{3}-\frac{1}{4} x^{2} $$ $$ \begin{array}{|c|c|} \hline \text { Term } & \text { Coefficient } \\ \hline 9.7 x^{7} & \\ \hline-3 x^{5} & \\ \hline x^{3} & \\ \hline-\frac{1}{4} x^{2} & \\ \hline \end{array} $$

Simplify each expression. Write each result using positive exponents only. $$ (7 x)^{-3} $$

Evaluate each expression. $$ (-3)^{2} $$

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

$$ \left(-5 x^{2}+3\right)+\left(2 x^{2}+1\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{6 x^{5}+3 x^{4}}{3 x^{4}} $$

Find the degree of each polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. See Examples 2 and 3. $$ x+2 $$

Simplify each expression. Write each result using positive exponents only. $$ \left(-\frac{1}{4}\right)^{-3} $$

Evaluate each expression. $$ -2^{4} $$

Multiply. \(-4 n^{3} \cdot 7 n^{7}\)

$$ \left(3 x^{2}+7\right)+\left(3 x^{2}+9\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{15 x^{2}-9 x^{5}}{x} $$

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

Simplify each expression. Write each result using positive exponents only. $$ \left(-\frac{1}{8}\right)^{-2} $$

Multiply. \(9 t^{6}\left(-3 t^{5}\right)\)

$$ \left(-3 y^{2}-4 y\right)+\left(2 y^{2}+y-1\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{-9 x^{4}+18 x^{5}}{6 x^{5}} $$

Find the degree of each polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. See Examples 2 and 3. $$ 9 m^{3}-5 m^{2}+4 m-8 $$

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

Multiply using the FOIL method. See Examples 1 through 3. $$ (y-6)(4 y-1) $$

Evaluate each expression. $$ (-2)^{4} $$

Multiply. \(\left(-3.1 x^{3}\right)\left(4 x^{9}\right)\)

$$ \left(7 x^{2}+2 x-9\right)+\left(-3 x^{2}+5\right) $$

Perform each division. See Examples 1 through 3. $$ \frac{14 m^{2}-27 m^{3}}{7 m} $$

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

Simplify each expression. Write each result using positive exponents only. $$ 4^{-1}+4^{-2} $$

Multiply using the FOIL method. See Examples 1 through 3. $$ (2 x-9)(x-11) $$

Evaluate each expression. $$ (-4)^{3} $$