91Ó°ÊÓ

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

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$2+3 i, 2-3 i,-5,2$$

Determine the vertical and slant asymptotes and sketch the graph of the rational function \(F\). $$F(x)=\frac{x^{2}+10}{2 x}$$

Use Descartes' Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. $$P(x)=x^{4}-1$$

Use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of \(P(x)\). $$P(x)=x^{3}+4 x^{2}-27 x-90, x+6$$

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. $$P(x)=(x+2)^{3}(x-6)^{10}$$

In Exercises 31 to \(42,\) write each expression as a complex number in standard form. $$\frac{5}{3+4 i}$$

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

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$6+5 i, 6-5 i, 2,3,5$$

Determine the vertical and slant asymptotes and sketch the graph of the rational function \(F\). $$F(x)=\frac{x^{2}-3 x-4}{x+3}$$