91Ó°ÊÓ

Perform the following operations. Write all results in lowest terms. See Section 1.3 $$ \frac{7}{10}-\frac{5}{12} $$

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline & {} & {91 .} & {92 .} & {93 .} & {94 .} & {95 .} & {96 .} \\ \hline \text {Two Numbers } & {4,7} & {} & {} & {} & {} \\ \hline \text {Their Product } & {28} & {12} & {20} & {8} & {16} & {-10} & {-24} \\ \hline \text {Their Sum } & {11} & {8} & {9} & {-9} & {-10} & {3} & {-5} \\ \hline \end{array} $$

Factor each trinomial completely. See Examples I through II and Section 6.2. \(5 x^{2} y^{2}+20 x y+1\)

In your own words, explain how to tell whether a binomial is a difference of squares. Then explain how to factor a difference of squares.

Find a positive value of \(c\) so that each trinomial is factorable. $$ t^{2}+8 t+c $$

Fill in the chart by finding two numbers that have the given product and sum. The first column is filled in for you. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline & {} & {91 .} & {92 .} & {93 .} & {94 .} & {95 .} & {96 .} \\ \hline \text {Two Numbers } & {4,7} & {} & {} & {} & {} \\ \hline \text {Their Product } & {28} & {12} & {20} & {8} & {16} & {-10} & {-24} \\ \hline \text {Their Sum } & {11} & {8} & {9} & {-9} & {-10} & {3} & {-5} \\ \hline \end{array} $$

Perform the following operations. Write all results in lowest terms. See Section 1.3 $$ \frac{5}{9}-\frac{5}{12} $$

Factor each trinomial completely. See Examples I through II and Section 6.2. \(3 a^{2} b^{2}+12 a b+1\)

In your own words, explain how to tell whether a binomial is a sum of cubes. Then explain how to factor a sum of cubes.

Find a positive value of \(c\) so that each trinomial is factorable. $$ y^{2}-4 y+c $$