91Ó°ÊÓ

Evaluate the expression and write the result in the form \(a+b i.\) $$\sqrt{-3} \sqrt{-12}$$

Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example \(3(a)\) $$P(x)=2 x^{4}+15 x^{3}+17 x^{2}+3 x-1$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer correct to two decimal places. $$y=x^{3}-12 x+9, \quad[-5,5] \text { by }[-30,30]$$

Find all zeros of the polynomial. $$P(x)=x^{4}+x^{3}+7 x^{2}+9 x-18$$

Find all zeros of the polynomial. $$P(x)=x^{4}-2 x^{3}-2 x^{2}-2 x-3$$

Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example \(3(a)\) $$P(x)=4 x^{5}-18 x^{4}-6 x^{3}+91 x^{2}-60 x+9$$

Let $$\begin{array}{r}P(x)=6 x^{7}-40 x^{6}+16 x^{5}-200 x^{4} \\\\-60 x^{3}-69 x^{2}+13 x-139\end{array}$$ Calculate \(P(7)\) by (a) using synthetic division and (b) substituting \(x=7\) into the polynomial and evaluating directly.

Find the intercepts and asymptotes, and then sketch a graph of the rational function. Use a graphing device to confirm your answer. $$r(x)=\frac{2 x^{2}+2 x-4}{x^{2}+x}$$

Evaluate the expression and write the result in the form \(a+b i.\) $$\sqrt{\frac{1}{3}} \sqrt{-27}$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer correct to two decimal places. $$y=2 x^{3}-3 x^{2}-12 x-32, \quad[-5,5] \text { by }[-60,30]$$