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Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: Simple (?) Polynomial Result
Replies: 10   Last Post: Jan 16, 2011 1:42 PM

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Anna R.

Posts: 3
Registered: 8/31/10
Simple (?) Polynomial Result
Posted: Aug 31, 2010 10:24 PM
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I'm working through a book and reached the result below. Verying the truth
of the statement is claimed to be easy but I've had little luck. Any ideas
how to proceed?

Let f(x) be a monic polynomial in Q[x] of degree n where n happens to be
even. Then there exist polynomials g(x) and h(x) such that f(x)=g(x)^2-h(x)
and g(x) has degree 1/2*n and h(x) has degree at most 1/2*n-1.

Thank you for any comments.





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