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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If ( x + 3) is a factor of x^3 - 2kx + k^2 , then k is:      Log On


   

Question 232400: If ( x + 3) is a factor of x^3 - 2kx + k^2 , then k is:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If ( x + 3) is a factor of x%5E3+-+2kx+%2B+k%5E2 , then (x+3) will divide into x%5E3+-+2kx+%2B+k%5E2 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 k%5E2%2B6k-27 zero will be our answer(s):
k%5E2%2B6k-27+=+0
This is a quadratic equation which we can solve by factoring or with the quadratic formula. It factors pretty easily:
%28k%2B9%29%28k-3%29+=+0
By the Zero Product Property one of these factor must be zero:
k%2B9+=+0 or k-3+=+0
Solving these we get:
k+=+-9 or k+=+3
So we have two possible values for k.