Let $f,g,h$ be polynomials over a field $F$.
$\forall t \in F$, $$f(x) = g(x)h(x) \iff f(x+t) = g(x+t)h(x+t)$$
The reverse direction is trivial. The forward is also obvious but I'm just wondering if there is a way to rigorously show it.
factors of polynomials
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$\begingroup$
polynomials
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0Can't you just substitute $x=u+t$? – 2017-01-24
1 Answers
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Both directions follow from substitution! No more work is necessary than that.
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0@Phantom Does this answer your question? – 2017-01-25