# Factor theorem

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#1
Show that ( X+2) cannot be a factor of f(x)=x^(2n)+4

I have ended up with 2^(2n)=-4. Am I correct in making the assumption that the LHS must be positive and therefore Proving the question?
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11 months ago
#2
(Original post by chatterclaw73)
Show that ( X+2) cannot be a factor of f(x)=x^(2n)+4

I have ended up with 2^(2n)=-4. Am I correct in making the assumption that the LHS must be positive and therefore Proving the question?
Sort of, just use the fact that the "root" is -2 and f(-2) is ... not zero
1
11 months ago
#3
(Original post by chatterclaw73)
Show that ( X+2) cannot be a factor of f(x)=x^(2n)+4

I have ended up with 2^(2n)=-4. Am I correct in making the assumption that the LHS must be positive and therefore Proving the question?
If you have to make the assumption, then you've haven't proven that it's positive. You're very close though. We know a square is never negative, so can you rewrite the LHS in the form of a square, using the rules of indices.
1
#4
(Original post by mqb2766)
Sort of, just use the fact that the "root" is -2 and f(-2) is ... not zero
Thanks.
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#5
(Original post by ghostwalker)
If you have to make the assumption, then you've haven't proven that it's positive. You're very close though. We know a square is never negative, so can you rewrite the LHS in the form of a square, using the rules of indices.
Thanks.
0
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