Chapter 4

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

\(15-26\) Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=\frac{1}{4}(x+1)^{3}(x-3) $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its x- and y-intercept(s). (c) Sketch its graph. $$ f(x)=6 x^{2}+12 x-5 $$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$ P(x)=x^{3}+3 x^{2}-x-3 $$

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

\(15-24=\) Find the quotient and remainder using long division. $$ \frac{x^{6}+x^{4}+x^{2}+1}{x^{2}+1} $$

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

\(15-26\) Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=\frac{1}{12}(x+2)^{2}(x-3)^{2} $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=x^{2}+2 x-1 $$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$ P(x)=x^{3}-4 x^{2}-11 x+30 $$

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

\(15-24=\) Find the quotient and remainder using long division. $$ \frac{2 x^{5}-7 x^{4}-13}{4 x^{2}-6 x+8} $$

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

\(15-26\) Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(x-1)^{2}(x+2)^{3} $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=x^{2}-8 x+8 $$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$ P(x)=x^{4}-5 x^{2}+4 $$

Find all horizontal and vertical asymptotes (if any). $$ s(x)=\frac{6 x^{2}+1}{2 x^{2}+x-1} $$

25-38 . Find the quotient and remainder using synthetic division. $$ \frac{x^{2}-5 x+4}{x-3} $$

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

\(15-26\) Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=x^{3}(x+2)(x-3)^{2} $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=3 x^{2}-6 x+1 $$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$ P(x)=x^{4}-2 x^{3}-3 x^{2}+8 x-4 $$

Find all horizontal and vertical asymptotes (if any). $$ s(x)=\frac{8 x^{2}+1}{4 x^{2}+2 x-6} $$

25-38 . Find the quotient and remainder using synthetic division. $$ \frac{x^{2}-5 x+4}{x-1} $$

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

\(15-26\) Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$ P(x)=(x-3)^{2}(x+1)^{2} $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=5 x^{2}+30 x+4 $$

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

Find all horizontal and vertical asymptotes (if any). $$ s(x)=\frac{(5 x-1)(x+1)}{(3 x-1)(x+2)} $$

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

\(27-40\) Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{3}-x^{2}-6 x $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=-x^{2}-3 x+3 $$

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

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

25-38 . Find the quotient and remainder using synthetic division. $$ \frac{4 x^{2}-3}{x+5} $$

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

\(27-40\) Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=x^{3}+2 x^{2}-8 x $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ f(x)=1-6 x-x^{2} $$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$ P(x)=4 x^{4}-25 x^{2}+36 $$

Find all horizontal and vertical asymptotes (if any). $$ r(x)=\frac{6 x^{3}-2}{2 x^{3}+5 x^{2}+6 x} $$

25-38 . Find the quotient and remainder using synthetic division. $$ \frac{x^{3}+2 x^{2}+2 x+1}{x+2} $$

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

\(27-40\) Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=-x^{3}+x^{2}+12 x $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ g(x)=3 x^{2}-12 x+13 $$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$ P(x)=2 x^{4}-x^{3}-19 x^{2}+9 x+9 $$

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

25-38 . Find the quotient and remainder using synthetic division. $$ \frac{3 x^{3}-12 x^{2}-9 x+1}{x-5} $$

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

\(27-40\) Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$ P(x)=-2 x^{3}-x^{2}+x $$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$ g(x)=2 x^{2}+8 x+11 $$