Suppose you were asked to factor the quadratic expression:

x² - 5x - 6

and you gave the answer as

(x - 6)(x + 1)

The first check is to to multiply them together using FOIL

x² + x - 6x - 6
x² - 5x - 6

And we see that it comes back to the original quadratic 
expression to factor.

The second check is to substitute an arbitrary number (other than 0 or 1)
into the original quadratic and also into your factorization.

Suppose we arbitrarily choose, say, x = 4

Substituting in the original quadratic eqxpression:

x² - 5x - 6

(4)² - 5(4) - 6

16 - 20 - 6

-10

Now we substitute x = 4 into your factorization:

(x - 6)(x + 1)

(4 - 6)(4 + 1)

(-2)(5)

-10

Both give us the same number -10.  That's the second check.

Edwin