91Ó°ÊÓ

Find all rational zeros of the given polynomial function \(f\). $$ f(x)=x^{5}+x^{4}-5 x^{3}+x^{2}-6 x $$

Find the vertical and horizontal asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph of \(f\). $$ f(x)=\frac{1}{x^{3}} $$

Use synthetic division to determine whether the indicated linear polynomial is a factor of the given polynomial function \(f\). If yes, find all other zeros and then give the complete factorization of \(f(x)\) $$ x-5 ; f(x)=2 x^{2}+6 x-25 $$

Use synthetic division to determine whether the indicated linear polynomial is a factor of the given polynomial function \(f\). If yes, find all other zeros and then give the complete factorization of \(f(x)\) $$ x+\frac{1}{2} ; f(x)=10 x^{2}-27 x+11 $$

Find all rational zeros of the given polynomial function \(f\). $$ f(x)=128 x^{6}-2 $$

Proceed as in Example 2 and use the Remainder Theorem to find \(r\) when \(f(x)\) is divided by the given linear polynomial. $$ f(x)=5 x^{3}+x^{2}-4 x-6 ; x+1 $$

Find the vertical and horizontal asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph of \(f\). $$ f(x)=\frac{8}{x^{4}} $$

Find all rational zeros of the given polynomial function \(f\). $$ f(x)=\frac{1}{2} x^{3}-\frac{9}{4} x^{2}+\frac{17}{4} x-3 $$

Find the vertical and horizontal asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph of \(f\). $$ f(x)=\frac{x}{x^{2}-1} $$

Use synthetic division to determine whether the indicated linear polynomial is a factor of the given polynomial function \(f\). If yes, find all other zeros and then give the complete factorization of \(f(x)\) $$ x-1 ; f(x)=x^{3}+x-2 $$