Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 55

$(p-5q)(p-2q)$

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}