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. $$f(x)=(x-2)^{2}(x+5)^{5}$$

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$-x^{3}+x ; x-5$$

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. $$h(s)=s^{2}-2 s+1$$

Find all the zeros, real and nonreal, of the polynomial. Then express \(p(x)\) as a product of linear factors. $$p(x)=x^{2}-\sqrt{3}$$

Use synthetic division to find the function values. \(f(x)=x^{3}-7 x+5 ;\) find \(f(3)\) and \(f(5)\)

Solve the rational inequality. $$\frac{x+2}{x-1} \leq 0$$

Determine the end behavior of the function. $$g(x)=-10 x^{3}+3 x^{2}+5 x-2$$

Find all real solutions of the polynomial equation. $$2 x^{3}-x^{2}-18 x=-9$$

Find all real solutions of the polynomial equation. $$x^{4}+x^{3}-x=1$$

Find an expression for a polynomial function \(f(x)\) having the given properties. There can be more than one correct anstoer. Degree 5 ; zeros at -2 and \(-1,\) each of multiplicity 1 zero at 5 of multiplicity 3