#### Answer

$x^{2}$ + 12x + 35 = (x + 5)( x + $7$)
Answer = (x $+$ $7$)

#### Work Step by Step

In $x^{2}$ + 12x + 35,
We look for factors of 35, whose sum is 12.
One factor is already given, 5.
Thus other factor is $\frac{35}{5}$ = 7.
Check:
Sum of 7 and 5 is 12,
and 7 $\times$ 5 =35.
Thus other factor = 7.
$x^{2}$ + 12x + 35 = (x + 5)( x + $7$)