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) $$ 3 t(t-4)=0 $$

For Problems \(1-30\), factor completely each of the trinomials and indicate any that are not factorable using integers. $$ a^{2}-a b-56 b^{2} $$

For Problems \(1-20\), use the difference-of-squares pattern to factor each of the following. (Objective 1) $$ 16 s^{2}-(3 t+1)^{2} $$

For Problems \(11-20\), factor each of the composite numbers into the product of prime numbers. For example, \(30=2 \cdot 3 \cdot 5\). (Objective 2 ) $$ 84 $$

For Problems \(1-30\), factor completely each of the trinomials and indicate any that are not factorable using integers. $$ a^{2}+2 a b-63 b^{2} $$

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) $$ (n+3)(n-12) $$

For Problems \(1-36\), find each product. $$ \left(-\frac{2}{7} a^{2}\right)\left(\frac{3}{5} a b^{3}\right) $$

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

For Problems \(11-20\), add the given polynomials. (Objective 2 ) $$ 15 a^{2} b^{2}-a b \text { and }-20 a^{2} b^{2}-6 a b $$

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) $$ (x+6)(x-6) $$