Chapter 11.2, Problem 1DE

To determine

To calculate: The pairs of binomials factors for trinomial expression $x^2+7x+12$ and complete the table by adding the all-possible factors which are given below,

PAIRS OF FACTORS	SUM OF FACTORS
$1,12$	$13$
$-1,-12$	$\boxed{}$
$2,6$	$\boxed{}$
$-2,-6$	$\boxed{}$
$3,4$	$\boxed{}$
$-3,-4$	$\boxed{}$

The coefficient of first term and constant term in the provided trinomial are positive, so only the factors $\boxed{}$ in the table is considered and therefore, the factors of $x^2+7x+12$ are $\left(x+3\right)\left(\boxed{}\right)$.