Chapter 3

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{4}-9 x^{2}+8$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$1-27 a^{3}$$

Factor by grouping. $$3 a x-3 b x-a y+b y$$

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

Raise each monomial to the indicated power. $$-(2 a b)^{4}$$

Perform the indicated operations. $$\left(2 x^{2}-7 x-1\right)+\left(-4 x^{2}-x+6\right)+\left(-7 x^{2}-4 x-1\right)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$(x+8)(x-6)=-24$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{4}-x^{2}-12$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$1-8 x^{3}$$

Factor by grouping. $$5 a x-5 b x-2 a y+2 b y$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(9 x-2 y)(9 x+2 y)$$

Raise each monomial to the indicated power. $$-(3 a b)^{4}$$

Perform the indicated operations. $$\left(5 x^{2}+x+4\right)+\left(-x^{2}+2 x+4\right)+\left(-14 x^{2}-x+6\right)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$4 a(a+1)=3$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$18 n^{4}+25 n^{2}-3$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$x^{3} y^{3}-1$$

Factor by grouping. $$2 a x+2 x+a y+y$$

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

Raise each monomial to the indicated power. $$-\left(x y^{2} z^{3}\right)^{6}$$

Perform the indicated operations. $$\left(7 x^{2}-x-4\right)-\left(9 x^{2}-10 x+8\right)+\left(12 x^{2}+4 x-6\right)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$-18 n^{2}-15 n+7=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$4 n^{4}+3 n^{2}-27$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$125 x^{3}+27 y^{3}$$

Factor by grouping. $$3 b x+3 x+b y+y$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(t-2)\left(t^{2}+7 t+2\right)$$

Raise each monomial to the indicated power. $$-\left(x y^{2} z^{3}\right)^{8}$$

Perform the indicated operations. $$\left(-6 x^{2}+2 x+5\right)-\left(4 x^{2}+4 x-1\right)+\left(7 x^{2}+4\right)$$

Set up an equation and solve each problem. Find two consecutive integers whose product is 72 .

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{4}-17 x^{2}+16$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$x^{6}-y^{6}$$

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

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x-4)\left(x^{2}+5 x-4\right)$$

Raise each monomial to the indicated power. $$\left(-5 a^{2} b^{2} c\right)^{3}$$

Perform the indicated operations. $$\left(n^{2}-7 n-9\right)-(-3 n+4)-\left(2 n^{2}-9\right)$$

Set up an equation and solve each problem. Find two consecutive even whole numbers whose product is 224 .

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$x^{4}-13 x^{2}+36$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$x^{6}+y^{6}$$

Factor by grouping. $$a x^{2}-2 x^{2}+3 a-6$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x+6)\left(2 x^{2}-x-7\right)$$

Raise each monomial to the indicated power. $$\left(-4 a b c^{4}\right)^{3}$$

Perform the indicated operations. $$\left(6 n^{2}-4\right)-\left(5 n^{2}+9\right)-(6 n+4)$$

Set up an equation and solve each problem. Find two integers whose product is 105 such that one of the integers is one more than twice the other integer.

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. $$2 t^{2}-8$$

Find all real number solutions for each equation. $$x^{2}-25=0$$

Factor by grouping. $$2 a c+3 b d+2 b c+3 a d$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(2 x-3)\left(x^{2}+6 x+10\right)$$

Raise each monomial to the indicated power. $$\left(-x y^{4} z^{2}\right)^{7}$$

Simplify by removing the inner parentheses first and working outward. $$3 x-[5 x-(x+6)]$$

Set up an equation and solve each problem. Find two integers whose product is 104 such that one of the integers is three less than twice the other integer.

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. $$14 w^{2}-29 w-15$$