Chapter 4

Divide the expression. $$\frac{5 x^{4}-15}{10 x}$$

Evaluate the expression by hand. $$ 8^{2 / 3} $$

Solve the rational equation (a) symbolically, (b) graphically, and (c) numerically $$ \frac{2 x}{x+2}=6 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{x^{3}-5 x+1}{4 x-5} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ f(x)=2 x^{3}-x+5 $$

Divide the expression. $$\frac{x^{2}-5 x}{5 x}$$

Solve the rational equation (a) symbolically, (b) graphically, and (c) numerically $$ \frac{3 x}{2 x-1}=3 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{6}{x^{2}} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ f(x)=-x^{4}+1 $$

Divide the expression. $$\frac{3 x^{4}-2 x^{2}-1}{3 x^{3}}$$

Evaluate the expression by hand. $$ 16^{-3 / 4} $$

Solve the rational equation (a) symbolically, (b) graphically, and (c) numerically $$ 2-\frac{5}{x}+\frac{2}{x^{2}}=0 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=x^{2}-x-2 $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ f(x)=\sqrt{x} $$

Divide the expression. $$\frac{5 x^{3}-10 x^{2}+5 x}{15 x^{2}}$$

Evaluate the expression by hand. $$ 25^{-3 / 2} $$

Solve the rational equation (a) symbolically, (b) graphically, and (c) numerically $$ \frac{1}{x^{2}}+\frac{1}{x}=2 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{x^{2}+1}{\sqrt{x-8}} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ f(x)=2 x^{3}-\sqrt[3]{x} $$

Divide the expression. $$\frac{x^{3}-4}{4 x^{3}}$$

Evaluate the expression by hand. $$ -81^{0.5} $$

Solve the rational equation (a) symbolically, (b) graphically, and (c) numerically $$ \frac{1}{x+1}+\frac{1}{x-1}=\frac{1}{x^{2}-1} $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{|x-1|}{x+1} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ f(x)=1-4 x-5 x^{4} $$

Divide the expression. $$\frac{2 x^{4}-3 x^{2}+4 x-7}{-4 x}$$

Evaluate the expression by hand. $$ 32^{1 / 5} $$

Solve the rational equation (a) symbolically, (b) graphically, and (c) numerically $$ \frac{4}{x-2}=\frac{3}{x-1} $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{4}{x}+1 $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ f(x)=5-4 x $$

Divide the expression. $$\frac{5 x\left(3 x^{2}-6 x+1\right)}{3 x^{2}}$$

Evaluate the expression by hand. $$ \left(9^{3 / 4}\right)^{2} $$

Find all real solutions. Check your results. $$ \frac{x+1}{x-5}=0 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{3-\sqrt{x}}{x^{2}+x} $$

Divide the expression. $$\frac{\left(1-5 x^{2}\right)(x+1)+x^{2}}{2 x}$$

Evaluate the expression by hand. $$ \left(4^{-1 / 2}\right)^{-4} $$

Find all real solutions. Check your results. $$ \frac{x-2}{x+3}=1 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{|x+1|}{x+1} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ g(t)=\frac{1}{1-t} $$

Divide the first polynomial by the second. State the quotient and remainder. $$x^{3}-2 x^{2}-5 x+6 \quad\quad\quad x-3$$

Let \(a_{n}\) be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients \(f(x)\) that satisfies the conditions. (b) Express \(f(x)\) in expanded form. Degree \(2 ; a_{n}=1\) zeros \(6 i\) and \(-6 i\)

Evaluate the expression by hand. $$ \frac{8^{5 / 6}}{8^{1 / 2}} $$

Find all real solutions. Check your results. $$ \frac{6(1-2 x)}{x-5}=4 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{3-\sqrt{x}}{x^{2}+x} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ g(t)=22 $$

Divide the first polynomial by the second. State the quotient and remainder. $$3 x^{3}-10 x^{2}-27 x+10 \quad\quad\quad x+2$$

Let \(a_{n}\) be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients \(f(x)\) that satisfies the conditions. (b) Express \(f(x)\) in expanded form. Degree \(3 ; a_{n}=5\) zeros \(2, i,\) and \(-i\)

Evaluate the expression by hand. $$ \frac{4^{-1 / 2}}{4^{3 / 2}} $$

Find all real solutions. Check your results. $$ \frac{2}{5(2 x+5)}+3=-1 $$

Determine whether \(f\) is a rational function and state its domain. $$ f(x)=\frac{x^{3}-3 x+1}{x^{2}-5} $$

Determine if the junction is a polynomial function. If it is, state its degree and leading coefficient a. $$ g(t)=|2 t| $$