2x² + 10x + 12
Let's see of we can factorise it by any algebraic expression.
Since the first and last terms aren't perfect squares this won't work !
Next, splitting the middle term ?
2x² + 4x + 6x + 12
2x(x + 2) + 6(x + 2)
(2x + 6)(x + 2)
Now, we can see that we can factorise the first factor into : 2(x + 3)
So, the final factors are
2(x + 3)(x+2)