Chapter 5 - Section 5.3 - Greatest Common Factors and Factoring by Grouping - Exercise Set - Page 349: 113

$4$.

The given expression is $(x+3)(x+?)=x^2+7x+12$ Factor the right hand side. $=x^2+7x+12$ $=x^2+4x+3x+12$ $=x(x+4)+3(x+4)$ $=(x+3)(x+4)$ Plug into the given expression. $(x+3)(x+?)=(x+3)(x+4)$ The $x+3$ values cancel, so we get that $x+?=x+4$. Cancelling x we get that the $?$ must equal $4$.