Originally Posted by

**Jameson** If only I could do that! The thing is we have only defined a very few things about polynomials. We have no theorem to justify that polynomials may be factored as such. When multiplying polynomials, the only information known about the product (from this text) is:

$\displaystyle P(x)Q(x) = c_0 + c_1 x + c_2 x^2 ... + c_n x^n + ...$, where for each n, $\displaystyle c_n = \sum_{i+j=n} a_i j_i$.

So, this proof has to be done term by term, so to speak as I cannot justify any operations on the product of two polynomials.