SOLUTION: If ( x + 3) is a factor of x^3

SOLUTION: If ( x + 3) is a factor of x^3 - 2kx + k^2 , then k is:

Question 232400: If ( x + 3) is a factor of x^3 - 2kx + k^2 , then k is:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If ( x + 3) is a factor of , then (x+3) will divide into evenly. And synthetic division is probably the easiest way to find out if (x+3) divides evenly:

-3 |  1   0   -2k   k^2
----     -3    9  -27+6k               
     -----------------------
      1  -3  9-2k   k^2+6k-27

When a division works out evenly, the remainder is zero. So the value(s) of k that makes zero will be our answer(s):

This is a quadratic equation which we can solve by factoring or with the quadratic formula. It factors pretty easily:

By the Zero Product Property one of these factor must be zero:
or
Solving these we get:
or
So we have two possible values for k.
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