Question

Please help with 1 & 2

Answer 1

First question:

I urge you to perform the division using the synthetic division method:

      ________________
-4  /   1   3   -6   -6   8
             -4    4     8  -8
       -----------------------
         1   -1   -2    2    0

Note that there is no remainder.  When this is the case, the divisor (here, that's -4) is a root of the given polynomial, and the value of that polynomial, g(-4), is 0.

If the remainder were not 0, then the remainder represents the value of the polynomial for that particular divisor.  For example, if x = -3, the remainder is -28.  We'd write that as g(-3) = -28.

But here, g(-4) = 0.