Chapter 3

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

Evaluate the expression and write the result in the form \(a+b i\) $$\left(7-\frac{1}{2} i\right)-\left(5+\frac{3}{2} i\right)$$

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

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

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. $$f(x)=2 x^{2}+x-6$$

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$(-4+i)-(2-5 i)$$

Find all rational zeros of the polynomial, and write the polynomial in factored form. $$P(x)=x^{3}-x^{2}-8 x+12$$

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

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. $$f(x)=2 x^{2}+x-6$$

Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. (GRAPH CANT COPY) $$P(x)=\frac{1}{3} x(x-5)^{2}$$

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$(-12+8 i)-(7+4 i)$$

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

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

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. $$f(x)=-4 x^{2}-16 x+3$$

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$6 i-(4-i)$$

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

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

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. $$f(x)=6 x^{2}+12 x-5$$

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$4(-1+2 i)$$

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

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

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

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

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

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

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

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

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

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$(7-i)(4+2 i)$$

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

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

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

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

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

Evaluate the expression and write the result in the form \(a+b i\) $$(5-3 i)(1+i)$$

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