Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3 - Page 255: 16

This expression is not factorable using integers.

To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$. In the case of $x^2-14x+32$, we are looking for two numbers whose product is $32$ and whose sum is $-14$. Unfortunately, there are no integers that meet these criteria, so this expression is not factorable using integers.