91Ó°ÊÓ

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

Evaluate the radical expression and express the result in the form \(a+b i\) $$\frac{1-\sqrt{-1}}{1+\sqrt{-1}}$$

Use the Factor Theorem to show that \(x-c\) is a factor of \(P(x)\) for the given value(s) of \(c\). $$P(x)=x^{3}+2 x^{2}-3 x-10, \quad c=2$$

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

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. $$r(x)=\frac{2 x(x+2)}{(x-1)(x-4)}$$

Find all zeros of the polynomial. $$P(x)=x^{5}-x^{4}+7 x^{3}-7 x^{2}+12 x-12$$

Use the Factor Theorem to show that \(x-c\) is a factor of \(P(x)\) for the given value(s) of \(c\). $$P(x)=2 x^{3}+7 x^{2}+6 x-5, \quad c=\frac{1}{2}$$

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. $$r(x)=\frac{x^{2}-2 x+1}{x^{2}+2 x+1}$$

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

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. $$f(x)=x^{3}-x$$