Chapter 3

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$4 x^{4}-13 x^{2}+9=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$n^{2}-26 n+168$$

Factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don't forget to look first for a common monomial factor. $$2 x^{5}-162 x$$

Factor completely. $$5 x(a-b)+y(a-b)$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(6-3 x)(6+3 x)$$

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

Perform the operations as described. Subtract \(-4 x^{2}+6 x-3\) from the sum of \(-3 x+4\) and \(9 x^{2}-6\)

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$3 x^{2}-46 x-32=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$t^{2}+3 t-180$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$a^{3}-64$$

Factor completely. $$x(x+2)+5(x+2)$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(7 x-4)^{2}$$

Raise each monomial to the indicated power. $$\left(2 a^{2} b^{3}\right)^{6}$$

Perform the operations as described. Subtract the sum of \(5 n^{2}-3 n-2\) and \(-7 n^{2}+n+2\) from \(-12 n^{2}-n+9\).

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$x^{4}-9 x^{2}=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$t^{2}-2 t-143$$

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

Factor completely. $$x(x-1)-3(x-1)$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(5 x-7)^{2}$$

Raise each monomial to the indicated power. $$\left(2 a^{3} b^{2}\right)^{6}$$

Perform the operations as described. Subtract the sum of \(-6 n^{2}+2 n-4\) and \(4 n^{2}-2 n+4\) from \(-n^{2}-n+1\).

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$2 x^{2}+x-3=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$t^{4}-5 t^{2}+6$$

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

Factor by grouping. $$a x+4 x+a y+4 y$$

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(6 x+7)(3 x-10)$$

Raise each monomial to the indicated power. $$\left(9 x y^{4}\right)^{2}$$

Perform the indicated operations. $$(5 x+2)+(7 x-1)+(-4 x-3)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$x^{3}+5 x^{2}-36 x=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$t^{4}+10 t^{2}+24$$

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

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

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(4 x-7)(7 x+4)$$

Raise each monomial to the indicated power. $$\left(8 x^{2} y^{5}\right)^{2}$$

Perform the indicated operations. $$(-3 x+1)+(6 x-2)+(9 x-4)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$12 x^{3}+46 x^{2}+40 x=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$10 x^{4}+3 x^{2}-4$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$27 x^{3}+64 y^{3}$$

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

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

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

Perform the indicated operations. $$(12 x-9)-(-3 x+4)-(7 x+1)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$5 x(3 x-2)=0$$

Factor completely each of the polynomials and indicate any that are not factorable using integers. $$3 x^{4}+7 x^{2}-6$$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. $$8 x^{3}+27 y^{3}$$

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

Find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. $$(x-4 y)(3 x+7 y)$$

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

Perform the indicated operations. $$(6 x+4)-(4 x-2)-(-x-1)$$

Solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. $$(3 x-1)^{2}-16=0$$