91Ó°ÊÓ

Sketch the graph of the rational function \(F\). (Hint: First examine the numerator and denominator to determine whether there are any common factors.) $$F(x)=\frac{x^{2}-x-12}{x^{2}-2 x-8}$$

Use synthetic division to show that \(c\) is a zero of \(P(x)\). $$P(x)=x^{3}+8, c=-2$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=4 x^{4}-35 x^{3}+71 x^{2}-4 x-6$$

Find a polynomial function \(P(x)\) with real coefficients that has the indicated zeros and satisfies the given conditions. Zeros: \(3,-5,2+i ;\) degree \(4 ; P(1)=48\)

Sketch the graph of the rational function \(F\). (Hint: First examine the numerator and denominator to determine whether there are any common factors.) $$F(x)=\frac{-2 x^{3}+6 x}{2 x^{2}-6 x}$$

In Exercises 43 to 50 , evaluate the power of \(i .\) $$i^{-34}$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=3 x^{6}-10 x^{5}-29 x^{4}+34 x^{3}+50 x^{2}-24 x-24$$

Use synthetic division to show that \(c\) is a zero of \(P(x)\). $$P(x)=3 x^{4}+8 x^{3}+10 x^{2}+2 x-20, c=-2$$

Use synthetic division to show that \(c\) is a zero of \(P(x)\). $$P(x)=x^{4}-2 x^{2}-100 x-75, c=5$$

Find a polynomial function \(P(x)\) with real coefficients that has the indicated zeros and satisfies the given conditions. Zeros: \(\frac{1}{2}, 1-i ;\) degree \(3 ; P(4)=140\)