Two Layers

To factor $2x^{2}+10x+12$, start with the greatest common factor. Every term is divisible by 2, so factor it out: $2\left(x^{2}+5x+6\right)$. Now factor the trinomial inside. The pair 2 and 3 has product 6 and sum 5, so the answer is $2\left(x+2\right)\left(x+3\right)$.

Always factor out the greatest common factor first. It makes the coefficients smaller, and it can show a trinomial or a special pattern that you can factor further.

A polynomial is factored completely when none of its factors can be factored any further over the integers. After you take out the GCF, look at every factor that is left. Check whether another factoring method applies to it.