91Ó°ÊÓ

Find a cubic polynomial in standard form with real coefficients, having the given zeros. Let the leading coefficient be \(1 .\) Do not use a calculator. 4 and \(2+i\)

For each complex number, (a) state the real part, (b) state the imaginary part, and (c) identify the number as one or more of the following: real, pure imaginary, or nonreal complex. $$-9 i$$

Solve each problem. Do not use a calculator. Find the maximum \(y\) -value on the graph of \(y=-16 x^{2}+32 x+100\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$\frac{10 x^{6}}{5 x^{3}}$$

Match the equation in Column I with its solution(s) in Column II. Do not use a calculator. (II) A. \(\pm 2 i\), B. \(\pm 2 \sqrt{2}\), C. \(\pm i \sqrt{2}\), D. 2, E. \(\pm \sqrt{2}\), F. \(-2\), G. \(\pm 2\), H. \(\pm 2 i \sqrt{2}\) (I) $$x^{2}=4$$

Find all real solutions. $$x^{3}-25 x=0$$

Find a cubic polynomial in standard form with real coefficients, having the given zeros. Let the leading coefficient be \(1 .\) Do not use a calculator. \(-3\) and \(6+2 i\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$\frac{6 x^{4}}{2 x^{3}}$$

For each complex number, (a) state the real part, (b) state the imaginary part, and (c) identify the number as one or more of the following: real, pure imaginary, or nonreal complex. $$3 i$$

Find all real solutions. $$x^{4}-x^{3}-6 x^{2}=0$$