91Ó°ÊÓ

Determine the multiplicities of the real zeros of the function. Comment on the behavior of the graph at the \(x\) -intercepts. Does the graph cross or just touch the \(x\) -axis? You may check your results with a graphing utility. $$h(x)=2 x^{3}-4 x^{2}+2 x$$

Find all the zeros, real and nonreal, of the polynomial. Then express \(p(x)\) as a product of linear factors. $$p(x)=x^{3}+7 x$$

Find the domain and the vertical and horizontal asymptotes (if any). $$h(x)=\frac{3 x^{2}}{x+1}$$

Write each polynomial in the form \(p(x)=d(x) q(x)+r(x),\) where \(p(x)\) is the given polynomial and \(d(x)\) is the given factor. You may use synthetic division wherever applicable. $$x^{2}+x+1 ; x+1$$

Determine whether the function is a polynomial function. If so, find the degree. If not, state the reason. $$f(x)=-x^{3}+3 x^{3}+1$$

Determine what type of symmetry, if any, the function illustrates. Classify the function as odd, even, or neither. $$g(x)=x^{4}+2 x^{2}-1$$

Find all the zeros, real and nonreal, of the polynomial. Then express \(p(x)\) as a product of linear factors. $$p(x)=x^{2}-\pi^{2}$$

Show that the given value of \(x\) is a zero of the polynomial. Use the zero to completely factor the polynomial. $$p(x)=3 x^{3}-2 x^{2}+3 x-2 ; x=\frac{2}{3}$$

Solve the polynomial inequality. $$(x-2)\left(x^{2}-4\right)<0$$

Determine whether the function is a polynomial function. If so, find the degree. If not, state the reason. $$f(s)=4 s^{5}-5 s^{3}+6 s-1$$