Chapter 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. $$-9 i$$

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. 4 and \(2+i\)

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

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) $$x^{2}=4$$

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

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. $$x^{4}-x^{3}-6 x^{2}=0$$

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. $$\frac{6 x^{4}}{2 x^{3}}$$

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) $$x^{2}=-4$$

Solve each problem. Do not use a calculator. Find the maximum \(y\) -value on the graph of \(y=-2 x^{2}+8 x-5\)

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. $$\pi$$

Find all real solutions. $$x^{4}-x^{2}=2 x^{2}+4$$

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. 5 and \(i\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$\frac{8 x^{9}}{3 x^{7}}$$

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) $$x^{2}+2=0$$

Solve each problem. Do not use a calculator. Find the minimum \(y\) -value on the graph of \(y=3 x^{2}-24 x+50\)

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. $$\sqrt{2}$$

Find all real solutions. $$x^{4}+5=6 x^{2}$$

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. \(-9\) and \(-i\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$-\frac{2 x^{5}}{7 x^{2}}$$

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) $$x^{2}-2=0$$

Solve each problem. Do not use a calculator. Find the minimum \(y\) -value on the graph of \(y=5 x^{2}+30 x+17\)

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. $$3+7 i$$

Find all real solutions. $$x^{3}-3 x^{2}-18 x=0$$

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

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) $$x^{2}=-8$$

Solve each problem. Do not use a calculator. $$\text { Solve }-4 x^{2}+5 x=1$$

For each quadratic function defined , (a) write the function in the form \(P(x)=a(x-h)^{2}+k,\) (b) give the vertex of the parabola, and (c) graph the function. Do not use a calculator. $$P(x)=x^{2}-2 x-15$$

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. $$-8+4 i$$

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

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. 0 and \(4-3 i\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$\frac{5 x^{3}+x^{2}}{3 x^{2}}$$

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) $$x^{2}=8$$

Solve each problem. Do not use a calculator. $$\text { Solve } x^{2}-6 x=7$$

For each quadratic function defined , (a) write the function in the form \(P(x)=a(x-h)^{2}+k,\) (b) give the vertex of the parabola, and (c) graph the function. Do not use a calculator. $$P(x)=x^{2}+2 x-15$$

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. $$i \sqrt{7}$$

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

Find a polynomial function \(P(x)\) of degree 3 with real coefficients that satisfies the given conditions. Do not use a calculator. Zeros of \(-3,-1,\) and \(4 ; \quad P(2)=5\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$\frac{8 x^{3}-5 x}{2 x}$$

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) $$x-2=0$$

Solve each problem. Do not use a calculator. $$\text { Solve } \frac{1}{2} x^{2}+3=6 x$$

For each quadratic function defined , (a) write the function in the form \(P(x)=a(x-h)^{2}+k,\) (b) give the vertex of the parabola, and (c) graph the function. Do not use a calculator. $$P(x)=-x^{2}-3 x+10$$

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. $$-i \sqrt{3}$$

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

Find a polynomial function \(P(x)\) of degree 3 with real coefficients that satisfies the given conditions. Do not use a calculator. Zeros of \(1,-1,\) and \(0 ; \quad P(2)=-3\)

Each expression. Apply the property \(\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\) if necessary. Do not use a calculator. $$\frac{7 x^{8}-6 x^{3}}{6 x^{2}}$$

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) $$x+2=0$$

Solve each problem. Do not use a calculator. $$\text { Solve } \frac{1}{4} x^{2}+x=1$$