91Ó°ÊÓ

For each polynomial, one or more zeros are given. Find all remaining zeros. \(P(x)=x^{3}-x^{2}-4 x-6 ; \quad 3\) is a zero.

Use the intermediate value theorem to show that each function has a real zero between the two numbers given. Then, use your calculator to approximate the zero to the nearest hundredth. $$P(x)=2 x^{4}-4 x^{2}+3 x-6 ; \quad 1.5 \text { and } 2$$

Use an end behavior diagram or to describe the end behavior of the graph of each function. Do not use a calculator. $$P(x)=2.74 x^{4}-3 x^{2}+x-2$$

Find all complex solutions of each equation. $$7 x^{3}+x=0$$

Solve each equation. For equations with real solutions, support your answers graphically. $$x^{2}=16$$

Write each expression in standard form. Do not use a calculator. $$(-7 i)(1+i)$$

Solve each problem. Maximizing Area A farmer has 1000 feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?

For each quadratic function defined , (a) write the function in the form \(P(x)=a(x-h)^{2}+k,\) (b) give the vertex of the parabola, and (c) graph the function. Do not use a calculator. $$P(x)=-2 x^{2}+6 x$$

Find all complex solutions of each equation. $$2 x^{3}-4 x=0$$

Use the intermediate value theorem to show that each function has a real zero between the two numbers given. Then, use your calculator to approximate the zero to the nearest hundredth. $$P(x)=x^{4}-4 x^{3}-x+1 ; \quad 0.3 \text { and } 1$$