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# Friedberg Linear Algebra pg 10, Vector Spaces

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1. http://imgur.com/WHvLari How is he saying that because m < n
g(x) = b_nx^n ...

I was expecting to rewrite f(x) in terms of g(x)
f(x) = g(x) + a_nx^n + ..

What the heck is he doing there?
2. He's just buffering up the polynomial with the smaller degree with zero monomials. He brings the two polynomials to the same degree to make the addition of these polynomials more intuitive.
3. ah - thanks - i had got that part about the build up but i got it now:
g(x) = b_nx^n + b_n-1x^n-1 ... + b_mx^m + ... b_0
All the n stuff is 0 because it's greater than m
so g(x) is actually the good old b_m to b_0 with no fancy tricks of any sort.
4. Yeah exactly! It's a simple thing that is obfuscated by dodgy notation. If it were up to me, I would have at least explicitly shown the mth coefficient in the "new" g(x) or stressed that it was the same polynomial or something.

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