Question 1092373
<pre>
There are two ways to do this problem.

Method 1:

The remainder theorem states: 

When a polynomial f(x) is divided by (x-r), the remainder is f(r).

Therefore f(4) = -8

 3(4)² + m(4) + 4 = -8
   3(16) + 4m + 4 = -8
      48 + 4m + 4 = -8
          52 + 4m = -8
               4m = -60
                m = -15

Method 2:

You can also do it by synthetic division

4 | 3       m         4
  |<u>        12     4(m+12)</u>
    3     m+12   4+4(m+12)

Then set the remainder equal to -8

         4+4(m+12) = -8
           4+4m+48 = -8
             52+4m = -8
                4m = -60
                 m = -15

Edwin</pre>