Chapter 3

Solve each of the equations. $$x^{2}+7 x=0$$

Find each quotient. $$\frac{-18 x^{2} y^{2} z^{6}}{x y z^{2}}$$

Simplify by removing the inner parentheses first and working outward. $$\left[2 n^{2}-\left(2 n^{2}-n+5\right)\right]+\left[3 n^{2}+\left(n^{2}-2 n-7\right)\right]$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$2 n^{2}-n-5$$

Find all real number solutions for each equation. $$54-6 x^{2}=0$$

Solve each of the equations. $$x^{2}+9 x=0$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x+1)^{3}$$

Find each quotient. $$\frac{-32 x^{4} y^{5} z^{8}}{x^{2} y z^{3}}$$

Simplify by removing the inner parentheses first and working outward. $$3 x^{2}-\left[4 x^{2}-2 x-\left(x^{2}-2 x+6\right)\right]$$

Set up an equation and solve each problem. Suppose that the length of one leg of a right triangle is 3 inches more than the length of the other leg. If the length of the hypotenuse is 15 inches, find the lengths of the two legs.

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$6 x^{2}+54$$

Find all real number solutions for each equation. $$x^{4}-81=0$$

Solve each of the equations. $$x^{2}-x=0$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x-4)^{3}$$

Find each quotient. $$\frac{a^{3} b^{4} c^{7}}{-a b c^{5}}$$

Simplify by removing the inner parentheses first and working outward. $$[7 x y-(2 x-3 x y+y)]-[3 x-(x-10 x y-y)]$$

Set up an equation and solve each problem. The lengths of the three sides of a right triangle are represented by consecutive even whole numbers. Find the lengths of the three sides.

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{5}-x$$

Find all real number solutions for each equation. $$x^{5}-x=0$$

Solve each of the equations. $$x^{2}-14 x=0$$

Find each quotient. $$\frac{-a^{4} b^{5} c}{a^{2} b^{4} c}$$

Simplify by removing the inner parentheses first and working outward. $$[9 x y-(4 x+x y-y)]-[4 y-(2 x-x y+6 y)]$$

Set up an equation and solve each problem. The area of a triangular sheet of paper is 28 square inches. One side of the triangle is 2 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$3 x^{2}+x-5$$

Find all real number solutions for each equation. $$6 x^{3}+24 x=0$$

Solve each of the equations. $$a^{2}=5 a$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(2 x+3)^{3}$$

Find each quotient. $$\frac{-72 x^{2} y^{4}}{-8 x^{2} y^{4}}$$

Simplify by removing the inner parentheses first and working outward. $$\left[4 x^{3}-\left(2 x^{2}-x-1\right)\right]-\left[5 x^{3}-\left(x^{2}+2 x-1\right)\right]$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$5 x^{2}+42 x-27$$

Find all real number solutions for each equation. $$4 x^{3}+12 x=0$$

Solve each of the equations. $$b^{2}=-7 b$$

Find each quotient. $$\frac{-96 x^{4} y^{5}}{12 x^{4} y^{4}}$$

Simplify by removing the inner parentheses first and working outward. $$\left[x^{3}-\left(x^{2}-x+1\right)\right]-\left[-x^{3}+\left(7 x^{2}-x+10\right)\right]$$

Discuss the role that factoring plays in solving equations.

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$2 n^{3}+6 n^{2}+10 n$$

Set up an equation and solve each of the following problems. The cube of a number equals nine times the same number. Find the number.

Solve each of the equations. $$-2 y=4 y^{2}$$

Find each quotient. $$\frac{14 a b^{3}}{-14 a b}$$

Explain how you would solve the equation \((x+6)(x-4)\) \(=0\) and also how you would solve \((x+6)(x-4)=\) \(-16 .\)

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$2 n^{3}+6 n^{2}+10 n$$

Set up an equation and solve each of the following problems. The cube of a number equals the square of the same number. Find the number.

Solve each of the equations. $$-6 x=2 x^{2}$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(3 x-2)^{3}$$

Find each quotient. $$\frac{-12 a b c^{2}}{12 b c}$$

Explain how you would solve the equation \(3(x-1)\) \((x+2)=0\) and also how you would solve the equation \(x(x-1)(x+2)=0\).

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$1-16 x^{4}$$

Set up an equation and solve each of the following problems. The combined area of two circles is \(80 \pi\) square centimeters. The length of a radius of one circle is twice the length of a radius of the other circle. Find the length of the radius of each circle.

Solve each of the equations. $$3 x^{2}+7 x=0$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(5 x+2)^{3}$$