91Ó°ÊÓ

Evaluate the radical expression and express the result in the form \(a+b i\) $$\frac{\sqrt{-36}}{\sqrt{-2} \sqrt{-9}}$$

Find all zeros of the polynomial. $$P(x)=x^{5}+x^{3}+8 x^{2}+8$$

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

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. $$y=x^{4}-18 x^{2}+32, \quad[-5,5] \text { by }[-100,100]$$

Evaluate the radical expression and express the result in the form \(a+b i\) $$\frac{\sqrt{-7} \sqrt{-49}}{\sqrt{28}}$$

Use the Factor Theorem to show that \(x-c\) is a factor of \(P(x)\) for the given value(s) of \(c\). $$P(x)=x^{4}+3 x^{3}-16 x^{2}-27 x+63, \quad c=3,-3$$

Find the intercepts and asymptotes, and then sketch a graph of the rational function and state the domain and range. Use a graphing device to confirm your answer. $$r(x)=\frac{4 x^{2}}{x^{2}-2 x-3}$$

Find the local maximum and minimum values of the function and the value of \(x\) at which each occurs. State each answer correct to two decimal places. $$f(x)=3+x+x^{2}-x^{3}$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. $$y=3 x^{5}-5 x^{3}+3, \quad[-3,3] \text { by }[-5,10]$$

A polynomial \(P\) is given. (a) Find all the real zeros of \(P\). (b) Sketch the graph of \(P\). $$P(x)=x^{3}-3 x^{2}-4 x+12$$