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    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?
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    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.
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    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.
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    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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