91Ó°ÊÓ

For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. $$\frac{3 x^{4}+3 x^{3}+2 x+2}{x+1}$$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. $$2 x^{3}-3 x^{2}-18 x-8=0$$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. $$3 x^{3}+11 x^{2}+8 x-4=0$$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. $$2 x^{4}-17 x^{3}+46 x^{2}-43 x+12=0$$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. $$4 x^{4}+8 x^{3}+19 x^{2}+32 x+12=0$$

For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive and negative solutions. $$x^{3}-3 x^{2}-2 x+4=0$$

For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive and negative solutions. $$2 x^{4}-x^{3}+4 x^{2}-5 x+1=0$$

For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. $$f(x)=\frac{x+2}{x-5}$$

For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. $$f(x)=\frac{x^{2}+1}{x^{2}-4}$$

For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. $$f(x)=\frac{3 x^{2}-27}{x^{2}+x-2}$$