Chapter 4

Find all horizontal and vertical asymptotes (if any). \(r(x)=\frac{x^{3}+3 x^{2}}{x^{2}-4}\)

Find the quotient and remainder using synthetic division. \(\frac{x^{2}-5 x+4}{x-1}\)

Find all rational zeros of the polynomial. $$ P(x)=x^{4}-x^{3}-23 x^{2}-3 x+90 $$

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{3}+2 x^{2}-8 x $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ Q(x)=x^{4}+2 x^{2}+1 $$

Find the quotient and remainder using synthetic division. \(\frac{3 x^{2}+5 x}{x-6}\)

Find all rational zeros of the polynomial. $$ P(x)=4 x^{4}-25 x^{2}+36 $$

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=-x^{3}+x^{2}+12 x $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ Q(x)=x^{4}+10 x^{2}+25 $$

Find the quotient and remainder using synthetic division. \(\frac{4 x^{2}-3}{x+5}\)

Find all rational zeros of the polynomial. $$ P(x)=x^{4}-x^{3}-5 x^{2}+3 x+6 $$

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=-2 x^{3}-x^{2}+x $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=x^{4}+3 x^{2}-4 $$

Find all rational zeros of the polynomial. $$P(x)=x^{4}+8 x^{3}+24 x^{2}+32 x+16$$

Find the quotient and remainder using synthetic division. \(\frac{x^{3}+2 x^{2}+2 x+1}{x+2}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{4}-3 x^{3}+2 x^{2} $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=x^{5}+7 x^{3} $$

Find all rational zeros of the polynomial. $$ P(x)=2 x^{3}+7 x^{2}+4 x-4 $$

Find the quotient and remainder using synthetic division. \(\frac{3 x^{3}-12 x^{2}-9 x+1}{x-5}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{5}-9 x^{3} $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=x^{5}+6 x^{3}+9 x $$

Find all rational zeros of the polynomial. $$ P(x)=4 x^{3}+4 x^{2}-x-1 $$

Find the quotient and remainder using synthetic division. \(\frac{x^{3}-8 x+2}{x+3}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{3}+x^{2}-x-1 $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=x^{6}+16 x^{3}+64 $$

Find all rational zeros of the polynomial. $$ P(x)=2 x^{3}-3 x^{2}-2 x+3 $$

Find the quotient and remainder using synthetic division. \(\frac{x^{4}-x^{3}+x^{2}-x+2}{x-2}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{3}+3 x^{2}-4 x-12 $$

\(31-40=\) Find a polynomial with integer coefficients that satisfies the given conditions. $$ P \text { has degree } 2, \text { and zeros } 1+i \text { and } 1-i $$

Find all rational zeros of the polynomial. $$ P(x)=4 x^{3}-7 x+3 $$

Find the quotient and remainder using synthetic division. \(\frac{x^{5}+3 x^{3}-6}{x-1}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=2 x^{3}-x^{2}-18 x+9 $$

\(31-40=\) Find a polynomial with integer coefficients that satisfies the given conditions. $$ P \text { has degree } 2, \text { and zeros } 1+i \sqrt{2} \text { and } 1-i \sqrt{2} $$

Find all rational zeros of the polynomial. $$ P(x)=8 x^{3}+10 x^{2}-x-3 $$

Find the quotient and remainder using synthetic division. \(\frac{x^{3}-9 x^{2}+27 x-27}{x-3}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=\frac{1}{8}\left(2 x^{4}+3 x^{3}-16 x-24\right)^{2} $$

\(31-40=\) Find a polynomial with integer coefficients that satisfies the given conditions. $$ Q \text { has degree } 3, \text { and zeros } 3,2 i, \text { and }-2 i $$

Find all rational zeros of the polynomial. $$ P(x)=4 x^{3}+8 x^{2}-11 x-15 $$

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. \(r(x)=\frac{4 x-4}{x+2}\)

Find the quotient and remainder using synthetic division. \(\frac{2 x^{3}+3 x^{2}-2 x+1}{x-\frac{1}{2}}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{4}-2 x^{3}-8 x+16 $$

\(31-40=\) Find a polynomial with integer coefficients that satisfies the given conditions. $$ Q \text { has degree } 3, \text { and zeros } 0 \text { and } i $$

Find all rational zeros of the polynomial. $$ P(x)=6 x^{3}+11 x^{2}-3 x-2 $$

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. \(r(x)=\frac{2 x+6}{-6 x+3}\)

Find the quotient and remainder using synthetic division. \(\frac{6 x^{4}+10 x^{3}+5 x^{2}+x+1}{x+\frac{2}{3}}\)

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{4}-2 x^{3}+8 x-16 $$

\(31-40=\) Find a polynomial with integer coefficients that satisfies the given conditions. $$ P \text { has degree } 3, \text { and zeros } 2 \text { and } i $$

Find all rational zeros of the polynomial. $$ P(x)=2 x^{4}-7 x^{3}+3 x^{2}+8 x-4 $$

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. \(s(x)=\frac{4-3 x}{x+7}\)

Find the quotient and remainder using synthetic division. \(\frac{x^{3}-27}{x-3}\)