Chapter 4

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=x(x-3)(x+2) $$

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

Find all rational zeros of the polynomial. $$ P(x)=x^{3}+4 x^{2}-3 x-18 $$

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(2 x-1)(x+1)(x+3) $$

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

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

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

Find all rational zeros of the polynomial. $$ P(x)=x^{3}-6 x^{2}+12 x-8 $$

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(x-3)(x+2)(3 x-2) $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ Q(x)=x^{2}-8 x+17 $$

Find all horizontal and vertical asymptotes (if any). \(s(x)=\frac{2 x+3}{x-1}\)

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

Find all rational zeros of the polynomial. $$ P(x)=x^{3}-x^{2}-8 x+12 $$

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=\frac{1}{5} x(x-5)^{2} $$

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

Find all horizontal and vertical asymptotes (if any). \(t(x)=\frac{x^{2}}{x^{2}-x-6}\)

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

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

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(x-1)^{2}(x-3) $$

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

Find all horizontal and vertical asymptotes (if any). \((x)=\frac{2 x-4}{x^{2}+2 x+1}\)

Find the quotient and remainder using long division. \(\frac{3 x^{4}-5 x^{3}-20 x-5}{x^{2}+x+3}\)

Find all rational zeros of the polynomial. $$ P(x)=x^{3}-4 x^{2}-7 x+10 $$

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=\frac{1}{4}(x+1)^{3}(x-3) $$

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

Find all horizontal and vertical asymptotes (if any). \(s(x)=\frac{6}{x^{2}+2}\)

Find the quotient and remainder using long division. \(\frac{6 x^{3}+2 x^{2}+22 x}{2 x^{2}+5}\)

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

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=\frac{1}{12}(x+2)^{2}(x-3)^{2} $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ Q(x)=x^{4}-625 $$

Find all horizontal and vertical asymptotes (if any). \(t(x)=\frac{(x-1)(x-2)}{(x-3)(x-4)}\)

Find the quotient and remainder using long division. \(\frac{9 x^{2}-x+5}{3 x^{2}-7 x}\)

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

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(x-1)^{2}(x+2)^{3} $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=16 x^{4}-81 $$

Find all horizontal and vertical asymptotes (if any). \(r(x)=\frac{6 x-2}{x^{2}+5 x-6}\)

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

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

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=x^{3}(x+2)(x-3)^{2} $$

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

Find all horizontal and vertical asymptotes (if any). \(s(x)=\frac{3 x^{2}}{x^{2}+2 x+5}\)

Find the quotient and remainder using long division. \(\frac{2 x^{5}-7 x^{4}-13}{4 x^{2}-6 x+8}\)

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

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(x-3)^{2}(x+1)^{2} $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=x^{3}+x^{2}+9 x+9 $$

Find all horizontal and vertical asymptotes (if any). \(t(x)=\frac{x^{2}+2}{x-1}\)

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

Find all rational zeros of the polynomial. $$ P(x)=x^{4}+6 x^{3}+7 x^{2}-6 x-8 $$

Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{3}-x^{2}-6 x $$

13- 30 . Factor the polynomial completely and find all its zeros. State the multiplicity of each zero. $$ P(x)=x^{6}-729 $$