How do you factor  12x^2 + 4x?

$4 x \left(3 x + 1\right)$
Simply look for what the two terms have in common. In this case, both $12 {x}^{2}$ and 4x have a 4x in common. (4 is the GCF of 12 and 4.) So you would factor the 4x out of the polynomial.