91Ó°ÊÓ

\(59-62\) . Find a polynomial of the specified degree that has the given zeros. Degree \(5 ; \quad\) zeros \(-2,-1,0,1,2\)

A polynomial P is given. (a) Factor P into linear and irreducible quadratic factors with real coefficients. (b) Factor P completely into linear factors with complex coefficients. \(P(x)=x^{3}-5 x^{2}+4 x-20\)

Height of a Ball If a ball is thrown directly upward with a velocity of 40 \(\mathrm{ft} / \mathrm{s}\) , its height (in feet) after \(t\) seconds is given by \(y=40 t-16 t^{2} .\) What is the maximum height attained by the ball?

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. $$ s(x)=\frac{x^{2}-2 x+1}{x^{3}-3 x^{2}} $$

Find a polynomial of degree 3 that has zeros \(1,-2,\) and 3 and in which the coefficient of \(x^{2}\) is 3 .

\(59-68\) Graph the polynomial and determine how many local maxima and minima it has. $$ y=x^{4}-5 x^{2}+4 $$

A polynomial \(P\) is given. (a) Find all the real zeros of \(P\) (b) Sketch the graph of \(P\) . $$ P(x)=x^{5}-x^{4}-5 x^{3}+x^{2}+8 x+4 $$

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. $$ t(x)=\frac{x^{3}-x^{2}}{x^{3}-3 x-2} $$

A polynomial \(P\) is given. (a) Find all the real zeros of \(P\) (b) Sketch the graph of \(P\) . $$ P(x)=x^{5}-x^{4}-6 x^{3}+14 x^{2}-11 x+3 $$

\(59-68\) Graph the polynomial and determine how many local maxima and minima it has. $$ y=1.2 x^{5}+3.75 x^{4}-7 x^{3}-15 x^{2}+18 x $$