How do you verify factoring is correct?

Multiply the factors together. You should get the original expression.

For example, if we are to factor

2x^2 + 4x

we would factor as

2x (x + 2).

Check this by multiplying back in

2x*x + 2x*2 = 2x^2 + 4x

which is what we started with, so we know we are correct.