## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(p-5q)(p-2q)$
The 2 numbers whose product is $ac= 1(10)=10$ and whose sum is $b= -7$ are $\left\{ -5,-2 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $p^2-7pq+10q^2 ,$ then the factored form is \begin{array}{l} p^2-5pq-2pq+10q^2 \\\\= (p^2-5pq)-(2pq-10q^2) \\\\= p(p-5q)-2q(p-5q) \\\\= (p-5q)(p-2q) .\end{array}