#### Answer

5$x^{2}$ -3x+13

#### Work Step by Step

(4$x^{2}$ - 6x + 12) + ($x^{2}$+ 3x +1)
The like terms are 4$x^{2}$ and $x^{2}$ containing the same variable to the same power($x^{2}$), as well as -6x and 3x (both containing x), and the constant terms 12 and 1.
We begin by grouping these pairs of like terms.
( 4$x^{2}$ + $x^{2}$)+ (-6x + 3x)+ (12+1)
= 5$x^{2}$ -3x+13