Chapter 3

Use long division to divide. Divisor \(x=1\) Dividend $$3 x^{2}-7 x+4$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{3 x}{x+1}$$

Determine the number of zeros of the polynomial function. $$f(x)=x-7$$

Write out the first 16 positive integer powers of \(i\) \(\left(i, i^{2}, i^{3}, \ldots, i^{16}\right)\), and write each as \(i,-i, 1\), or \(-1 .\) What pattern do you observe?

Use the Rational Zero Test to list all possible rational zeros of \(f\). Then use a graphing utility to graph the function. Use the graph to help determine which of the possible rational zeros are actual zeros of the function. $$f(x)=x^{3}+x^{2}-4 x-4$$

Use long division to divide. Divisor \(x-4\) Dividend $$5 x^{2}-17 x-12$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{x}{x-2}$$

Determine the number of zeros of the polynomial function. $$g(x)=x^{4}-256$$

Use the Rational Zero Test to list all possible rational zeros of \(f\). Then use a graphing utility to graph the function. Use the graph to help determine which of the possible rational zeros are actual zeros of the function. $$f(x)=2 x^{4}-x^{2}-6$$

Use long division to divide. Divisor \(x+3\) Dividend $$2 x^{2}+10 x+12$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{x-7}{5-x}$$

Determine the number of zeros of the polynomial function. $$h(x)=-x^{3}+2 x^{2}-5$$

Find the real numbers \(a\) and \(b\) such that the equation is true. $$a+b i=7+12 i$$

Find the rational zeros of the polynomial function. $$f(x)=x^{3}-\frac{3}{2} x^{2}-\frac{23}{2} x+6$$

Use long division to divide. Divisor \(x+5\) Dividend $$2 x^{2}+x-11$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{1-5 x}{1+2 x}$$

Determine the number of zeros of the polynomial function. $$f(t)=-2 t^{5}-3 t^{3}+1$$

Find the real numbers \(a\) and \(b\) such that the equation is true. $$a+b i=-2-5 i$$

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

Use long division to divide. Divisor \(2 x^{2}-1\) Dividend $$2 x^{3}+6 x^{2}-x-3$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{3 x^{2}+1}{x^{2}+9}$$

Determine the number of zeros of the polynomial function. $$f(x)=6 x-x^{4}$$

Find the real numbers \(a\) and \(b\) such that the equation is true. $$(a+3)+(b-1) i=7-4 i$$

Find the rational zeros of the polynomial function. $$f(x)=4 x^{4}-17 x^{2}+4$$

Use long division to divide. Divisor \(3 x^{2}-2\) Dividend $$3 x^{3}-12 x^{2}-2 x+8$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{3 x^{2}+x-5}{x^{2}+1}$$

Determine the number of zeros of the polynomial function. $$f(x)=3-7 x^{2}-5 x^{4}+9 x^{6}$$

Find the real numbers \(a\) and \(b\) such that the equation is true. $$(a+6)+2 b i=6-5 i$$

Find the rational zeros of the polynomial function. $$f(x)=-2 x^{4}+13 x^{3}-21 x^{2}+2 x+8$$

Use long division to divide. Divisor \(x+2\) Dividend $$x^{4}+5 x^{3}+6 x^{2}-x-2$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{5}{(x+4)^{2}}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=x^{2}+16$$

Write the complex number in standard form and find its complex conjugate. $$9+\sqrt{-16}$$

Find all real zeros of the function. $$f(x)=x^{3}-6 x^{2}+11 x-6$$

Use long division to divide. Divisor \(x^{2}-4\) Dividend $$x^{4}+2 x^{3}-3 x^{2}-8 x-4$$

Find the domain of the function and identify any horizontal and vertical asymptotes. $$f(x)=\frac{1}{(x-1)^{2}}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=x^{2}+36$$

Write the complex number in standard form and find its complex conjugate. $$2+\sqrt{-25}$$

Find all real zeros of the function. $$g(x)=x^{3}-4 x^{2}-x+4$$

Use long division to divide. Divisor \(x+4\) Dividend $$7 x+3$$

Use the graph of \(y=x^{3}\) to sketch the graph of the function. $$f(x)=x^{3}-2$$

Find any (a) vertical, (b) horizontal, and (c) slant asymptotes of the graph of the function. Then sketch the graph of \(f\). $$f(x)=\frac{x^{2}-7 x+12}{x-3}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$h(x)=x^{2}-5 x+5$$

Write the complex number in standard form and find its complex conjugate. $$-3-\sqrt{-12}$$

Find all real zeros of the function. $$h(t)=t^{3}+12 t^{2}+21 t+10$$

Use long division to divide. Divisor \(2 x+3\) Dividend $$8 x-5$$

Use the graph of \(y=x^{3}\) to sketch the graph of the function. $$f(x)=(x+3)^{3}$$

Find any (a) vertical, (b) horizontal, and (c) slant asymptotes of the graph of the function. Then sketch the graph of \(f\). $$f(x)=\frac{x+3}{x^{2}-9}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$g(x)=x^{2}+10 x+23$$

Write the complex number in standard form and find its complex conjugate. $$1+\sqrt{-8}$$