Question

(X^2-4) divided by (x+4)

Answer 1

Keep in mind that x^2 - 4 is a "special product," whose factors are

x - 2 and x + 2.  In this particular case this fact doesn't help much.

So, use either long division or synthetic division here:

Rewrite x^2 - 4 as x^2 - 0x - 4, whose coefficients are 1, 0 and -4.

Use -4 as the divisor in synth. div.; it comes from the divisor (x + 4).

Then the synth. div. looks like this:

-4    /     1    0    -4

                 -4     16

       --------------------

            1      -4    12

This result tells us that the quotient is 1x - 4 with a remainder of 12.

An interesting fact is that if you evaluate x^2 - 4 or x^2 - 0x - 4 at x = -4, the result will be 12 (same as the remainder shown above).