Question 7746
First, you ought to use parentheses around the numerator and denominator to make it absolutely clear.

(2x^2 - 32)/(x-4)  If you were to perform the indicated division either by long division or by synthetic division, you would get a result of: 2x + 8.

I find it easier to factor the numerator and cancel like factors in the numerator and denominator.

{{{(2x^2 - 32)/(x - 4) = 2(x + 4)(x - 4)/(x - 4)}}} Cancel the (x-4)'s

{{{(2x^2 - 32)/(x - 4) = 2(x + 4)}}} Simplify.

{{{(2x^2 - 32)/(x - 4) = 2x + 8}}}

You can perform the suggested test on the erroneous answer (2x - 8) and on the correct solution (2x + 8) by substituting a convenient value for x in both cases.