91Ó°ÊÓ

Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example \(3(\mathrm{a}) .\) $$ P(x)=3 x^{3}-5 x^{2}-8 x-2 $$

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

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

\(53-56\) . Use the Factor Theorem to show that \(X-c\) is a factor of \(P(x)\) for the given value(s) of \(c .\) $$ P(x)=x^{3}+2 x^{2}-3 x-10, \quad c=2 $$

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

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

\(53-56\) . Use the Factor Theorem to show that \(X-c\) is a factor of \(P(x)\) for the given value(s) of \(c .\) $$ P(x)=2 x^{3}+7 x^{2}+6 x-5, \quad c=\frac{1}{2} $$

\(51-58\) Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. $$ y=x^{4}+4 x^{3}, \quad[-5,5] \text { by }[-30,30] $$

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

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