91Ó°ÊÓ

For Problems \(21-44\), 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. (Objective 1) $$ 2 x^{5}-162 x $$

For Problems \(1-74\), find each indicated product. Remember the shortcut for multiplying binomials and the other special patterns we discussed in this section. (Objectives 1-4) $$ (6-3 x)(6+3 x) $$

For Problems \(31-56\), factor completely each of the trinomials and indicate any that are not factorable using integers. $$ 6 x^{2}+13 x-33 $$

For Problems \(45-56\), use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. (Objective 2) $$ a^{3}-64 $$

For Problems \(1-54\), solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. (Objective 1) $$ 3 x^{2}-46 x-32=0 $$

For Problems \(31-56\), factor completely each of the trinomials and indicate any that are not factorable using integers. $$ 6-35 x-6 x^{2} $$

For Problems \(25-50\), factor completely. $$ x(y+2)+3(y+2) $$

For Problems \(37-58\), raise each monomial to the indicated power. (Objective 2) $$ \left(2 a^{2} b^{3}\right)^{6} $$

For Problems \(41-46\), perform the operations as described. (Objective 2) Subtract the sum of \(5 n^{2}-3 n-2\) and \(-7 n^{2}+n+2\) from \(-12 n^{2}-n+9\).

For Problems \(41-46\), perform the operations as described. (Objective 2) Subtract the sum of \(-6 n^{2}+2 n-4\) and \(4 n^{2}-2 n+4\) from \(-n^{2}-n+1\).