91Ó°ÊÓ

Find the vertical and slant asymptotes for the graph of the given rational function. Find \(x\) - and \(y\) -intercepts of the graph. Sketch the graph \(f\). $$ f(x)=\frac{x^{2}-3 x-10}{x} $$

Verify that the indicated complex number is a zero of the given polynomial function \(f\). Proceed as in Example 7 to find all other zeros and then give the complete factorization of \(f(x)\). $$ \frac{1}{2} i ; f(x)=12 x^{3}+8 x^{2}+3 x+2 $$

Find all real zeros of the given polynomial function \(f\). Then factor \(f(x)\) using only real numbers. $$ f(x)=x^{4}-2 x^{3}-23 x^{2}+24 x+144 $$

Use synthetic division to find the quotient \(q(x)\) and remainder \(r\) when \(f(x)\) is divided by the given linear polynomial. $$ f(x)=4 x^{2}-8 x+6 ; x-\frac{1}{2} $$

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

Find all real zeros of the given polynomial function \(f\). Then factor \(f(x)\) using only real numbers. $$ f(x)=x^{5}+4 x^{4}-6 x^{3}-24 x^{2}+5 x+20 $$

Use synthetic division to find the quotient \(q(x)\) and remainder \(r\) when \(f(x)\) is divided by the given linear polynomial. $$ f(x)=x^{3}-x^{2}+2 ; x+3 $$

Use synthetic division to find the quotient \(q(x)\) and remainder \(r\) when \(f(x)\) is divided by the given linear polynomial. $$ f(x)=4 x^{3}-3 x^{2}+2 x+4 ; x-7 $$

Find all real zeros of the given polynomial function \(f\). Then factor \(f(x)\) using only real numbers. $$ f(x)=18 x^{5}+75 x^{4}+47 x^{3}-52 x^{2}-11 x+3 $$

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