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Question 927008: Let P(x) = kx^3 + 2k^2x^2 + k^3. Find the sum of all real numbers k for which x-2 is a factor of P(x).
Please help!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Using the remainder theorem, if x-k is a factor of P(x), then P(k) = 0.
So that means if x-2 is a factor of P(x), then P(2) = 0
Plug x = 2 into P(x) and set it equal to 0
P(x) = kx^3 + 2k^2x^2 + k^3
P(x) = k(2)^3 + 2k^2(2)^2 + k^3
P(x) = 8k+8k^2+k^3
0 = 8k+8k^2+k^3
8k+8k^2+k^3 = 0
k^3+8k^2+8k = 0
Now we solve for k
k^3+8k^2+8k = 0
k*(k^2+8k+8) = 0
I'll let you finish up. One of those factors will give you complex (nonreal) solutions.
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