91Ó°ÊÓ

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. $$P(x)=(2 x-3)^{4}(x-1)^{15}$$

Use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of \(P(x)\). $$P(x)=2 x^{3}+x^{2}-3 x-1, x+1$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=x^{3}+3 x^{2}-6 x-8$$

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$\frac{1}{2}, 4-i, 4+i$$

Use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of \(P(x)\). $$P(x)=3 x^{3}+4 x^{2}-27 x-36, x-4$$

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. $$P(x)=(5 x+10)^{6}(x-2.7)^{5}$$

Determine the vertical and slant asymptotes and sketch the graph of the rational function \(F\). $$F(x)=\frac{x^{2}-4 x-5}{2 x+5}$$

In Exercises 31 to \(42,\) write each expression as a complex number in standard form. $$\frac{5 i}{2-3 i}$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=x^{3}-19 x-30$$

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