Chapter 3

Find all real zeros of the function. $$f(x)=x^{3}-4 x^{2}+5 x-2$$

Use long division to divide. Divisor \(2 x^{2}+1\) Dividend $$6 x^{3}+10 x^{2}+x+8$$

Use the graph of \(y=x^{3}\) to sketch the graph of the function. $$f(x)=(x+1)^{3}-4$$

Find any (a) vertical, (b) horizontal, and (c) slant asymptotes of the graph of the function. Then sketch the graph of \(f\). $$f(x)=\frac{x^{2}}{x+1}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=x^{4}-81$$

Write the complex number in standard form and find its complex conjugate. $$-21$$

Find all real zeros of the function. $$C(x)=2 x^{3}+3 x^{2}-1$$

Use long division to divide. Divisor \(x-4\) Dividend $$2 x^{3}-8 x^{2}+3 x-9$$

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

Find any (a) vertical, (b) horizontal, and (c) slant asymptotes of the graph of the function. Then sketch the graph of \(f\). $$f(x)=\frac{x^{3}+x}{x^{2}-1}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(t)=t^{4}-625$$

Find all real zeros of the function. $$f(x)=3 x^{3}-19 x^{2}+33 x-9$$

Use long division to divide. Divisor \(x^{2}-1\) Dividend $$x^{3}-27$$

Use the graph of \(y=x^{4}\) to sketch the graph of the function. $$f(x)=(x+3)^{4}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$g(x)=x^{3}+5 x$$

Write the complex number in standard form and find its complex conjugate. $$-6 i+i^{2}$$

Find all real zeros of the function. $$f(x)=x^{4}-11 x^{2}+18$$

Use long division to divide. Divisor \(x^{2}+1\) Dividend $$x^{3}-9$$

Use the graph of \(y=x^{4}\) to sketch the graph of the function. $$f(x)=x^{4}-4$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$g(x)=x^{3}+7 x$$

Write the complex number in standard form and find its complex conjugate. $$4 i^{2}-2 i^{3}$$

Find all real zeros of the function. $$P(t)=t^{4}-19 t^{2}+48$$

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

Use the graph of \(y=x^{4}\) to sketch the graph of the function. $$f(x)=3-x^{4}$$

Compare the graph of the quadratic function with the graph of \(y=x^{2}\). $$f(x)=5 x^{2}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$h(x)=x^{3}-11 x^{2}-15 x+325$$

Write the complex number in standard form and find its complex conjugate. $$-5 i^{5}$$

Find all real solutions of the polynomial equation. $$z^{4}-z^{3}-2 z-4=0$$

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

Use the graph of \(y=x^{4}\) to sketch the graph of the function. $$f(x)=\frac{1}{2}(x-1)^{4}$$

Compare the graph of the quadratic function with the graph of \(y=x^{2}\). $$f(x)=-\frac{1}{4} x^{2}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$h(x)=x^{3}-3 x^{2}+4 x-2$$

Write the complex number in standard form and find its complex conjugate. $$(-i)^{3}$$

Find all real solutions of the polynomial equation. $$x^{4}-13 x^{2}-12 x=0$$

Use long division to divide. Divisor \(x^{2}-2 x+1\) Dividend $$2 x^{5}-8 x^{3}+4 x-1$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=-x^{3}+1$$

Compare the graph of the quadratic function with the graph of \(y=x^{2}\). $$f(x)=-(x+1)^{2}+1$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$g(x)=x^{3}-6 x^{2}+13 x-10$$

Write the complex number in standard form and find its complex conjugate. $$(\sqrt{-6})^{2}+3$$

Find all real solutions of the polynomial equation. $$2 y^{4}+7 y^{3}-26 y^{2}+23 y-6=0$$

Use long division to divide. Divisor \(x^{3}-1\) Dividend $$x^{5}+7$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=\frac{1}{3} x^{3}+5 x$$

Compare the graph of the quadratic function with the graph of \(y=x^{2}\). $$f(x)=3(x-2)^{2}-1$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=x^{3}-2 x^{2}-11 x+52$$

Write the complex number in standard form and find its complex conjugate. $$(\sqrt{-4})^{2}-5$$

Find all real solutions of the polynomial equation. $$2 x^{4}-11 x^{3}-6 x^{2}+64 x+32=0$$

Use synthetic division to divide. Divisor \(x+4\) Dividend $$2 x^{3}+5 x^{2}-7 x+20$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$g(x)=6-4 x^{2}+x-3 x^{5}$$

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$f(x)=3 x^{2}$$

Compare the graph of \(f(x)=1 / x\) with the graph of \(g\). $$g(x)=f(x)-2=\frac{1}{x}-2$$