Chapter 3

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(t)=t^{3}-3 t^{2}-15 t+125$$

Perform the indicated operation and write the result in standard form. $$(-4+3 i)+(6-2 i)$$

Find all real solutions of the polynomial equation. $$x^{5}-x^{4}-3 x^{3}+5 x^{2}-2 x=0$$

Use synthetic division to divide. Divisor \(x-8\) Dividend $$3 x^{3}-23 x^{2}-12 x+32$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=2 x^{5}-5 x+7.5$$

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

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

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=x^{3}+8 x^{2}+20 x+13$$

Perform the indicated operation and write the result in standard form. $$(13-2 i)+(-5+6 i)$$

Find all real solutions of the polynomial equation. $$x^{5}-7 x^{4}+10 x^{3}+14 x^{2}-24 x=0$$

Use synthetic division to divide. Divisor \(x+2\) Dividend $$4 x^{3}-9 x+8 x^{2}-18$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=4 x^{8}-2$$

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$f(x)=16-x^{2}$$

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

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=x^{3}+24 x^{2}+214 x+740$$

Perform the indicated operation and write the result in standard form. $$(12+5 i)-(7-i)$$

(a) list the possible rational zeros of \(f_{t}\) (b) sketch the graph of \(f\) so that some of the possible zeros in part (a) can be discarded, and (c) determine all real zeros of \(f\). $$f(x)=32 x^{3}-52 x^{2}+17 x+3$$

Use synthetic division to divide. Divisor \(x-2\) Dividend $$9 x^{3}-16 x-18 x^{2}+32$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$h(x)=1-x^{6}$$

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$h(x)=x^{2}-9$$

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

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

Perform the indicated operation and write the result in standard form. $$(3+2 i)-(6+13 i)$$

(a) list the possible rational zeros of \(f_{t}\) (b) sketch the graph of \(f\) so that some of the possible zeros in part (a) can be discarded, and (c) determine all real zeros of \(f\). $$f(x)=4 x^{3}+7 x^{2}-11 x-18$$

Use synthetic division to divide. Divisor \(x+10\) Dividend $$-x^{3}+75 x-250$$

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

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$f(x)=(x+5)^{2}-6$$

Compare the graph of \(f(x)=4 / x^{2}\) with the graph of \(g\). $$g(x)=f(x)+3=\frac{4}{x^{2}}+3$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$h(x)=x^{3}+9 x^{2}+27 x+35$$

Perform the indicated operation and write the result in standard form. $$(-2+\sqrt{-8})+(5-\sqrt{-50})$$

Use the Intermediate Value Theorem to show that the function has at least one zero in the interval \([a, b] .\) (You do not have to approximate the zero.) $$f(x)=x^{3}+2 x-5, \quad[1,2]$$

Use synthetic division to divide. Divisor \(x-6\) Dividend $$3 x^{3}-16 x^{2}-72$$

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

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$f(x)=(x-6)^{2}+3$$

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

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(s)=2 s^{3}-5 s^{2}+12 s-5$$

Perform the indicated operation and write the result in standard form. $$(5+\sqrt{-18})-(3+\sqrt{-32})$$

Use the Intermediate Value Theorem to show that the function has at least one zero in the interval \([a, b] .\) (You do not have to approximate the zero.) $$f(x)=x^{5}-3 x+3, \quad[-2,-1]$$

Use synthetic division to divide. Divisor \(x+3\) Dividend $$x^{4}-4 x^{3}-7 x^{2}+22 x+24$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$h(t)=-\frac{2}{3}\left(t^{2}-5 t+3\right)$$

Compare the graph of \(f(x)=4 / x^{2}\) with the graph of \(g\). $$g(x)=-f(x)=-\frac{4}{x^{2}}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=16 x^{3}-20 x^{2}-4 x+15$$

Perform the indicated operation and write the result in standard form. $$-\left(\frac{3}{2}+\frac{5}{2} i\right)+\left(\frac{5}{3}+\frac{11}{3} i\right)$$

Use the Intermediate Value Theorem to show that the function has at least one zero in the interval \([a, b] .\) (You do not have to approximate the zero.) $$f(x)=x^{4}-3 x^{2}-10, \quad[2,3]$$

Use synthetic division to divide. Divisor \(x+2\) Dividend $$6 x^{4}-15 x^{3}-11 x$$

Describe the right-hand and left-hand behavior of the graph of the polynomial function. $$f(s)=-\frac{2}{8}\left(s^{3}+5 s^{2}-7 s+1\right)$$

Sketch the graph of the quadratic function. Identify the vertex and intercepts. $$h(x)-x^{2}-4 x+2$$

Compare the graph of \(f(x)=4 / x^{2}\) with the graph of \(g\). $$g(x)=\frac{1}{8} f(x)=\frac{1}{2 x^{2}}$$

Find all the zeros of the function and write the polynomial as a product of linear factors. $$f(x)=9 x^{3}-15 x^{2}+11 x-5$$

Perform the indicated operation and write the result in standard form. $$(1.6+3.2 i)+(-5.8+4.3 i)$$