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The Integer Root Theorem

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How to guess integer roots of polynomials in $ \mathbb{Z} [x]$.

Given polynomial $ p(x) = x^n + a_{n-1}x^{n-1} + \dots + a_1 x + a_0$ with coefficients $ a_{n-1},\dots,a_1,a_0 \in \mathbb{Z}$, thus any integer root $ x_0$ of $ p(x)$ divides $ a_0$.

As $ a_0$ has only a finit number of divisors one can determine all integer roots of $ p(x)$.

Examples:

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  automatically generated 7/ 8/2004