Chapter 3

Find all real number solutions for each equation. $$x^{2}-1=0$$

Factor by grouping. $$2 b x+c y+c x+2 b y$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(3 x+4)\left(2 x^{2}-2 x-6\right)$$

Raise each monomial to the indicated power. $$\left(-x^{2} y^{4} z^{5}\right)^{5}$$

Simplify by removing the inner parentheses first and working outward. $$7 x-[2 x-(-x-4)]$$

Set up an equation and solve each problem. The perimeter of a rectangle is 32 inches, and the area is 60 square inches. Find the length and width of the rectangle.

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. $$12 x^{2}+7 x y-10 y^{2}$$

Find all real number solutions for each equation. $$9 x^{2}-49=0$$

Factor by grouping. $$a x-b y+b x-a y$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(4 x-1)\left(3 x^{2}-x+6\right)$$

Find each quotient. $$\frac{9 x^{4} y^{5}}{3 x y^{2}}$$

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

Set up an equation and solve each problem. Suppose that the length of a certain rectangle is two centimeters more than three times its width. If the area of the rectangle is 56 square centimeters, find its length and width.

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. $$8 x^{2}+2 x y-y^{2}$$

Find all real number solutions for each equation. $$4 y^{2}=25$$

Factor by grouping. $$2 a^{2}-3 b c-2 a b+3 a c$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(5 x-2)\left(6 x^{2}+2 x-1\right)$$

Find each quotient. $$\frac{12 x^{2} y^{7}}{6 x^{2} y^{3}}$$

Simplify by removing the inner parentheses first and working outward. $$4 x^{2}-\left[-x^{2}-\left(5 x^{2}-6\right)\right]$$

Set up an equation and solve each problem. The sum of the squares of two consecutive integers is 85. Find the integers.

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. $$18 n^{3}+39 n^{2}-15 n$$

Find all real number solutions for each equation. $$8 x^{2}-32=0$$

Factor by grouping. $$x^{2}+9 x+6 x+54$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$\left(x^{2}+2 x+1\right)\left(x^{2}+3 x+4\right)$$

Find each quotient. $$\frac{25 x^{5} y^{6}}{-5 x^{2} y^{4}}$$

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

Set up an equation and solve each problem. The sum of the areas of two circles is \(65 \pi\) square feet. The length of a radius of the larger circle is 1 foot less than twice the length of a radius of the smaller circle. Find the length of a radius of each circle.

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. $$n^{2}+18 n+77$$

Find all real number solutions for each equation. $$3 x^{2}-108=0$$

Factor by grouping. $$x^{2}-2 x+5 x-10$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$\left(x^{2}-x+6\right)\left(x^{2}-5 x-8\right)$$

Find each quotient. $$\frac{56 x^{6} y^{4}}{-7 x^{2} y^{3}}$$

Simplify by removing the inner parentheses first and working outward. $$-7 n^{2}-\left[3 n^{2}-\left(-n^{2}-n+4\right)\right]$$

Set up an equation and solve each problem. The combined area of a square and a rectangle is 64 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 2 centimeters more than its width. Find the dimensions of the square and the rectangle.

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. $$n^{2}-17 n+60$$

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

Factor by grouping. $$2 x^{2}+8 x+x+4$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$\left(2 x^{2}+3 x-4\right)\left(x^{2}-2 x-1\right)$$

Find each quotient. $$\frac{-54 a b^{2} c^{3}}{-6 a b c}$$

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

Set up an equation and solve each problem. The Ortegas have an apple orchard that contains 90 trees. The number of trees in each row is 3 more than twice the number of rows. Find the number of rows and the number of trees per row.

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. $$(x+5)^{2}-y^{2}$$

Find all real number solutions for each equation. $$4 x^{3}=64 x$$

Factor by grouping. $$3 x^{2}+18 x-2 x-12$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$\left(3 x^{2}-2 x+1\right)\left(2 x^{2}+x-2\right)$$

Find each quotient. $$\frac{-48 a^{3} b c^{5}}{-6 a^{2} c^{4}}$$

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

Set up an equation and solve each problem. The lengths of the three sides of a right triangle are represented by consecutive 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. $$36 a^{2}-12 a+1$$

Find all real number solutions for each equation. $$20-5 x^{2}=0$$