Question 927008
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.
------------------------------------------------------------------------------------------------------------------------


If you need more one-on-one help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).


Alternatively, please consider visiting my website: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Any amount is greatly appreciated as it helps me a lot. This donation is to support free tutoring. Thank you.


Jim

------------------------------------------------------------------------------------------------------------------------