Chapter 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. $$f(x)=5 x^{2}+30 x+4$$

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

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

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. $$P(x)=x^{3}+x^{2}+9 x+9$$

Evaluate the expression and write the result in the form \(a+b i\) $$(3-4 i)(5-12 i)$$

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

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

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

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$\left(\frac{2}{3}+12 i\right)\left(\frac{1}{6}+24 i\right)$$

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

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

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

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

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

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

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

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

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$(-2+i)(3-7 i)$$

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

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

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

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$i^{3}$$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$P(x)=3 x^{4}-10 x^{3}-9 x^{2}+40 x-12$$

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

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

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$(2 i)^{4}$$

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

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$h(x)=3-4 x-4 x^{2}$$

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

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

Use transformations of the graph of \(y=\frac{1}{x}\) to graph the rational function, as in Example 2. $$r(x)=\frac{1}{x-1}$$

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

Evaluate the expression and write the result in the form \(a+b i\) $$i^{100}$$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$P(x)=4 x^{3}+4 x^{2}-x-1$$

Find the maximum or minimum value of the function. $$f(x)=x^{2}+x+1$$

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

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