91Ó°ÊÓ

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 \(P(x)=D(x) \cdot Q(x)+R(x).\) $$P(x)=2 x^{3}-3 x^{2}-2 x, \quad D(x)=2 x-3$$

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

Find the real and imaginary parts of the complex number. $$-6+4 i$$

The graph of a quadratic function \(f\) 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 \(f\). $$f(x)=-\frac{1}{2} x^{2}-2 x+6$$ (GRAPH CAN'T COPY)

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

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

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. $$P(x)=x^{3}-2 x^{2}+2 x$$

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 \(P(x)=D(x) \cdot Q(x)+R(x).\) $$P(x)=x^{4}-x^{3}+4 x+2, \quad D(x)=x^{2}+3$$