Question 252530
<pre><font size = 4 color = "indigo"><b>

                                 5x -     5
           --------------------------------  
x² + x + 1 ) 5x³ + 0x² +         Mx +     N
             5x³ + 5x² +         5x
             ----------------------
                  -5x² +     (M-5)x +     N
                  -5x² -         5x -     5
                  -------------------------
                         [(M-5)+5]x + (N+5)

Remainder = [(M-5)+5]x + (N+5) = 0
              [M-5+5]x + (N+5) = 0
                    Mx +  N+5  = 0

The only this can be identically 0 for all values of x
is for the coefficient of x to be 0.

                      So M=0, so
                  
                         N+5 = 0
                           N = -5

Therefore M + N = 0 + (-5) = -5  choice c

Edwin</pre>