SOLUTION: determine p so that 4q+3 is a factor of 20q^3+23q^2-10q+p

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Question 706025: determine p so that 4q+3 is a factor of 20q^3+23q^2-10q+p
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If we factor a 4 out of 4q+3 we get
4%28q%2B3%2F4%29
So if (4q+3) is a factor of our polynomial then so will %28q%2B4%2F3%29. This fact is useful because we can more obviously use synthetic division with the %28q%2B3%2F4%29:
-3/4 |   20   23   -10   p
------       -15    -6  12 
        --------------------
         20    8   -16  12+p

In order for %28q%2B3%2F4%29 (and therefore (4q+3)) to be a factor, the remainder, 12+p, must be zero. So "p" must be -12.