91Ó°ÊÓ

Use the Remainder Theorem to find \(P(c)\). $$P(x)=x^{5}+20 x^{2}-1, c=-5$$

Determine the \(x\) -intercepts of the graph of \(P\). For each \(x\) -intercept, use the Even and Odd Powers of \((x-c)\) Theorem to determine whether the graph of \(P\) crosses the \(x\) -axis or intersects but does not cross the \(x\) -axis. $$P(x)=(x+2)(x-6)^{2}$$

Find the slant asymptote of each rational function. $$F(x)=\frac{x^{3}-1}{x^{2}}$$

In Exercises 31 to \(42,\) write each expression as a complex number in standard form. $$\frac{4-8 i}{4 i}$$

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$0, i,-i$$

In Exercises 31 to \(42,\) write each expression as a complex number in standard form. $$\frac{1}{7+2 i}$$

Determine the \(x\) -intercepts of the graph of \(P\). For each \(x\) -intercept, use the Even and Odd Powers of \((x-c)\) Theorem to determine whether the graph of \(P\) crosses the \(x\) -axis or intersects but does not cross the \(x\) -axis. $$P(x)=-(x-3)^{2}(x-7)^{5}$$

Use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of \(P(x)\). $$P(x)=x^{3}+2 x^{2}-5 x-6, x-2$$

Use Descartes' Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. $$P(x)=x^{5}-32$$

Determine the vertical and slant asymptotes and sketch the graph of the rational function \(F\). $$F(x)=\frac{x^{2}-4}{x}$$