Answer
$(4x+1)(3x+4)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two integers whose product is $48$ and whose sum is $19$. A little searching determines that these numbers are $3$ and $16$. Therefore, we can express the middle term $19x$ as $3x+16x$ and proceed to factoring by grouping:
$12x^{2}+19x+4$
=$12x^{2}+3x+16x+4$
=$3x(4x+1)+4(4x+1)$
=$(4x+1)(3x+4)$
