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Does anyone know of a relationship between the constant term of a polynomial and the roots of the polynomial? Specifically, if we know the constant term, is it possible for a root which divides the constant to be a root of the polynomial? Thanks in advance.

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  • $\begingroup$ The Rational Root Theorem is probably what you are looking for. $\endgroup$ – Yiyuan Lee Jul 15 '14 at 6:15
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http://www.sosmath.com/algebra/factor/fac10/fac10.html

The most important part is written slightly lower on the page:

Suppose $P(x)=a_nx^n + \dots + a_0$

is a polynomial with integer coefficients, and $x=\frac pq$ is a rational zero of $P(x)$. Then $p$ divides $a_0$ and $q$ divides $a_n$

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