91Ó°ÊÓ

Use Descartes' Rule of Signs to determine the number of positive and negative zeros of \(p\). You need not find the zeros. $$p(x)=4 x^{4}-5 x^{3}+6 x-3$$

Let \(x-\frac{1}{2}\) be a factor of a polynomial function \(p(x) .\) Find \(p\left(\frac{1}{2}\right).\)

Sketch the polynomial function using transformations. $$h(x)=-\frac{1}{2}(x+1)^{3}-2$$

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

Solve the rational inequality. $$\frac{x+1}{x^{2}-9}<0$$

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

Sketch a graph of the rational function. Indicate any vertical and horizontal asymptote(s) and all intercepts. $$f(x)=\frac{x}{(x-3)(x-1)}$$

Find an expression for a polynomial \(p(x)\) with real coefficients that satisfies the given conditions. There may be more than one possible answer. Degree \(4 ; x=-1\) and \(x=-3\) are zeros of multiplicity 1 and \(x=\frac{1}{3}\) is a zero of multiplicity 2

For what value(s) of \(k\) do you get a remainder of 15 when you divide \(k x^{3}+2 x^{2}-10 x+3\) by \(x+2 ?\)

Use Descartes' Rule of Signs to determine the number of positive and negative zeros of \(p\). You need not find the zeros. $$p(x)=x^{4}+6 x^{3}-7 x^{2}+2 x-1$$