Chapter 4

Find all real solutions. Check your results. $$ \frac{2}{x-1}+1=\frac{4}{x^{2}-1} $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{3}{x^{2}-5} $$

Divide the expression. $$\frac{20 x^{4}+6 x^{3}-2 x^{2}+15 x-2}{5 x-1}$$

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=x^{2}+11 $$

Use positive exponents to rewrite. $$ (\sqrt[3]{y^{2}})^{-5} $$

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

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{3 x^{2}}{x^{2}-9} $$

Divide the expression. $$\frac{5 x^{4}-2 x^{2}+6}{x^{2}+2}$$

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=3 x^{3}+3 x $$

Use positive exponents to rewrite. $$ \sqrt{x} \cdot \sqrt[3]{x} $$

Find all real solutions. Check your results. $$ \frac{1}{x+2}=\frac{4}{4-x^{2}}-1 $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{x^{4}+1}{x^{2}+3 x-10} $$

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

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=2 x^{3}+10 x $$

Use positive exponents to rewrite. $$ (\sqrt[5]{z})^{-3} $$

Find all real solutions. Check your results. $$ \frac{1}{x-3}+1=\frac{6}{x^{2}-9} $$

Divide the expression. $$\frac{8 x^{3}+10 x^{2}-12 x-15}{2 x^{2}-3}$$

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=x^{4}+5 x^{2}+4 $$

Use positive exponents to rewrite. $$ \sqrt{y \cdot \sqrt{y}} $$

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

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{x^{2}+2 x+1}{2 x^{2}-3 x-5} $$

Divide the expression. $$\frac{3 x^{4}-2 x^{2}-5}{3 x^{2}-5}$$

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=x^{4}+4 x^{2} $$

Use positive exponents to rewrite. $$ \frac{\sqrt[3]{x}}{\sqrt{x}} $$

Find all real solutions. Check your results. $$ \frac{1}{2 x+1}+\frac{1}{2 x-1}=\frac{2}{4 x^{2}-1} $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{6 x^{2}-x-2}{2 x^{2}+x-6} $$

Divide the expression. $$\frac{2 x^{4}-x^{3}+4 x^{2}+8 x+7}{2 x^{2}+3 x+2}$$

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=x^{3}+2 x^{2}+16 x+32 $$

Use radical notation to rewrite. $$ a^{-3 / 4} b^{1 / 2} $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{3 x(x+2)}{(x+2)(x-1)} $$

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

Complete the following. (a) Find all zeros of \(f(x)\) (b) Write the complete factored form of \(f(x)\) $$ f(x)=x^{4}+2 x^{3}+x^{2}+8 x-12 $$

Use radical notation to rewrite. $$ a^{-2 / 3} b^{3 / 5} $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{x}{x^{3}-x} $$

Use the equation (Dividend) = (Divisor)(Quotient) + (Remainder) to complete the following. $$\begin{aligned}&\frac{x^{3}-8 x^{2}+15 x-6}{x-2}=x^{2}-6 x+3 \text { imphes }\\\&(x-2)\left(x^{2}-6 x+3\right)=?\end{aligned}$$

Solve the polynomial equation. $$ x^{3}+x=0 $$

Use radical notation to rewrite. $$ \left(a^{1 / 2}+b^{1 / 2}\right)^{1 / 2} $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{x^{2}-9}{x+3} $$

Solve the polynomial equation. $$ 2 x^{3}-x+1=0 $$

Use radical notation to rewrite. $$ \left(a^{3 / 4}-b^{3 / 2}\right)^{1 / 3} $$

Find any horizontal or vertical asymptotes. $$ f(x)=\frac{2 x^{2}-3 x+1}{2 x-1} $$

Use division to express the (Dividend) as (Divisor)(Quotient) \(+\) (Remainder) $$\frac{x^{2}-3 x+1}{x-2}$$

Solve the polynomial equation. $$ x^{3}=2 x^{2}-7 x+14 $$

Solve the equation. Check your answers. $$ \sqrt{x+2}=x-4 $$

Use division to express the (Dividend) as (Divisor)(Quotient) \(+\) (Remainder) $$\frac{2 x^{2}-x+2}{x+4}$$

Solve the polynomial equation. $$ x^{2}+x+2=x^{3} $$

Solve the equation. Check your answers. $$ \sqrt{2 x+1}=13 $$

Let a be a positive constant. Match \(f(x)\) with its graph \((a-d)\) without using a calculator. $$ f(x)=\frac{2 x+a}{x-1} $$

Use division to express the (Dividend) as (Divisor)(Quotient) \(+\) (Remainder) $$\frac{2 x^{3}+x^{2}-2 x}{2 x+1}$$

Solve the polynomial equation. $$ x^{4}+5 x^{2}=0 $$