91Ó°ÊÓ

For Problems \(1-54\), solve each equation. You will need to use the factoring techniques that we discussed throughout this chapter. (Objective 1) $$ (x+8)(x-6)=-24 $$

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) $$ 1-8 x^{3} $$

For Problems \(31-56\), factor completely each of the trinomials and indicate any that are not factorable using integers. $$ 7 n^{2}+31 n+12 $$

For Problems \(51-68\), factor by grouping. $$ a x-2 x+a y-2 y $$

For Problems \(47-56\), perform the indicated operations. $$ \left(5 x^{2}+x+4\right)+\left(-x^{2}+2 x+4\right)+\left(-14 x^{2}-x+6\right) $$

For Problems \(37-58\), raise each monomial to the indicated power. (Objective 2) $$ -(3 a b)^{4} $$

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) $$ (t+3)\left(t^{2}-3 t-5\right) $$

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

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) $$ x^{3} y^{3}-1 $$

For Problems \(31-56\), factor completely each of the trinomials and indicate any that are not factorable using integers. $$ 10 x^{4}+3 x^{2}-4 $$