How do we check our answer? Can you demonstrate with an example?

Do you mean something like this?

x

^{2}+ 3x + 2 = 0(x + 2)(x + 1) = 0

so x + 2 = 0 and x + 1 = 0

then, x = -2 and x = -1

to check these, just plug them into the original equation in place of x:

(-2)2 + 3(-2) + 2 = 0 ??

4 + -6 + 2 = 0 ??

-2 + 2 = 0 ??

0 = 0 true!

repeat with x = -1 ....