91Ó°ÊÓ

A polynomial P is given. (a) Find all zeros of P, real and complex. (b) Factor P completely. \(P(x)=x^{4}+4 x^{2}\)

\(3-8=\) Two polynomials \(P\) and \(D\) are given. Use either synthetic or long division to divide \(P(x)\) by \(D(x),\) and express \(P\) in the form \(P(x)=D(x) \cdot Q(x)+R(x)\) $$ P(x)=2 x^{3}-3 x^{2}-2 x, \quad D(x)=2 x-3 $$

A polynomial P is given. (a) Find all zeros of P, real and complex. (b) Factor P completely. \(P(x)=x^{5}+9 x^{3}\)

List all possible rational zeros given by the Rational Zeros Theorem (but don' t check to see which actually are zeros). $$ Q(x)=x^{4}-3 x^{3}-6 x+8 $$

\(3-8=\) Two polynomials \(P\) and \(D\) are given. Use either synthetic or long division to divide \(P(x)\) by \(D(x),\) and express \(P\) in the form \(P(x)=D(x) \cdot Q(x)+R(x)\) $$P(x)=4 x^{3}+7 x+9, \quad D(x)=2 x+1$$

The graph of a quadratic function is given. (a) Find the coordinates of the vertex. (b) Find the maximum or minimum value of f. (c) Find the domain and range of f. $$ f(x)=-x^{2}+6 x-5 $$

The following questions are about the rational function $$ I(x)=\frac{(x+1)(x-2)}{(x+2)(x-3)} $$ The function \(r\) has horizontal asymptote \(y=\) ___________

\(5-8\) Sketch the graph of each function by transforming the graph of an appropriate function of the form \(y=x^{n}\) from Figure 2 . Indicate all \(x\) - and \(y\) -intercepts on each graph. $$ \begin{array}{ll}{\text { (a) } P(x)=x^{3}-8} & {\text { (b) } Q(x)=-x^{3}+27} \\\ {\text { (c) } R(x)=-(x+2)^{3}} & {\text { (d) } S(x)=\frac{1}{2}(x-1)^{3}+4}\end{array} $$

List all possible rational zeros given by the Rational Zeros Theorem (but don' t check to see which actually are zeros). $$ R(x)=2 x^{5}+3 x^{3}+4 x^{2}-8 $$

A polynomial P is given. (a) Find all zeros of P, real and complex. (b) Factor P completely. \(P(x)=x^{3}-2 x^{2}+2 x\)