SOLUTION: Find the values of k if 3(x+3)^4 - (k+x)^2 has a factor x+1

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Question 1183612: Find the values of k if 3(x+3)^4 - (k+x)^2 has a factor x+1
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If a polynomial in x has x%2B1 as a factor, it can be written as %28x%2B1%29Q%28x%29 where Q%28x%29 is another polynomial,
and the value of the original polynomial is
%28-1%2B1%29Q%28-1%29=0%2AQ%28-1%29=0 for x=-1
Then, for x=-1 we have
3%28-1%2B3%29%5E4-%28k%2B%28-1%29%29%5E2=0
3%282%29%5E4-%28k-1%29%5E2=0
3%2A16-%28k-1%29%5E2=0
%28k-1%29%5E2=3%2A16
k-1=%22+%22+%2B-+sqrt%283%2A16%29
k=1+%2B-+sqrt%283%2A16%29
highlight%28k=1+%2B-+4sqrt%283%29%29

You can also solve the problem the long, cumbersome, treacherous way, but that increases the risk of errors.