SOLUTION: IS x+9 A FACTOR of x^2+11x+21??? I SAY NO BECAUSE THE REMAINDER IS 3 AM I CORRECT??????

Looks like you're right.  Whether by regular 
long divsion:

         x+ 2 
x+9)x²+11x+21
    x²+ 9x
        2x+21
        2z+18
            3 

or by the shorter synthetic division:

-9|1 11  21
  |  -9 -18
   1  2   3

the remainder is 3.  In order for it to be a factor,
the remainder would have to be 0, not something else,
like, for instance, 3.

Edwin

Yes! Other than the shouting (typing in CAPS), your answer is perfect!