Chapter 6

Solve each inequality and graph its solution set on a number line. $$ (x+2)(x-1)>0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ x^{2}-4 x-6=0 $$

Simplify and reduce each expression. $$ \frac{2 \pm \sqrt{20}}{4} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x^{2}-4 x-60=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}-9 x=0 $$

Label each statement true or false. Every complex number is a real number.

Solve each inequality and graph its solution set on a number line. $$ (x-2)(x+3)>0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ x^{2}-8 x-4=0 $$

Simplify and reduce each expression. $$ \frac{4 \pm \sqrt{20}}{6} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x^{2}+6 x-16=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}+5 x=0 $$

Label each statement true or false. Every real number is a complex number.

Solve each inequality and graph its solution set on a number line. $$ (x+1)(x+4)<0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 3 x^{2}+23 x-36=0 $$

Simplify and reduce each expression. $$ \frac{-6 \pm \sqrt{27}}{3} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x^{2}-14 x=-40 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}=-3 x $$

Label each statement true or false. The real part of the complex number \(6 i\) is 0 .

Solve each inequality and graph its solution set on a number line. $$ (x-3)(x-1)<0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ n^{2}+22 n+105=0 $$

Simplify and reduce each expression. $$ \frac{-9 \pm \sqrt{54}}{3} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x^{2}-18 x=-72 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}=15 x $$

Label each statement true or false. Every complex number is a pure imaginary number.

Solve each inequality and graph its solution set on a number line. $$ (2 x-1)(3 x+7) \geq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ x^{2}-18 x=9 $$

Simplify and reduce each expression. $$ \frac{6 \pm \sqrt{18}}{9} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x^{2}-5 x-50=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 3 y^{2}+12 y=0 $$

Label each statement true or false. The sum of two complex numbers is always a complex number.

Solve each inequality and graph its solution set on a number line. $$ (3 x+2)(2 x-3) \geq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ x^{2}+20 x=25 $$

Simplify and reduce each expression. $$ \frac{12 \pm \sqrt{32}}{8} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x^{2}+3 x-18=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 6 y^{2}-24 y=0 $$

Label each statement true or false. The imaginary part of the complex number 7 is 0 .

Solve each inequality and graph its solution set on a number line. $$ (x+2)(4 x-3) \leq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 2 x^{2}-3 x+4=0 $$

Simplify and reduce each expression. $$ \frac{-10 \pm \sqrt{75}}{10} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x(x+7)=8 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 5 n^{2}-9 n=0 $$

Label each statement true or false. The sum of two complex numbers is sometimes a real number.

Solve each inequality and graph its solution set on a number line. $$ (x-1)(2 x-7) \leq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 3 y^{2}-2 y+1=0 $$

Simplify and reduce each expression. $$ \frac{-4 \pm \sqrt{8}}{4} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ x(x-1)=30 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 4 n^{2}+13 n=0 $$

Label each statement true or false. The sum of two pure imaginary numbers is always a pure imaginary number.

Solve each inequality and graph its solution set on a number line. $$ (x+1)(x-1)(x-3)>0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 135+24 n+n^{2}=0 $$