Prove that p(x) cannot have more than m zeros , where $p(x)$ is a polynominal of degree m and $p(x) ∈ \mathbb{K} [x]$ and $\mathbb{K}$ is a field

Question

The question is as stated in the title: Prove that p(x) cannot have more than m zeros $p(x)$, where $p(x)$ is a polynominal of degree m and $p(x) ∈ \mathbb{K} [x]$ and $\mathbb{K}$ is a field . (where the zeros are counted with multiplcities)

I am also given the hint : Use the fact that $\mathbb{K} [x]$ is a factorial ring

Note that if $\alpha$ is a root for $p(x)$, then $(x - \alpha) \mid p(x)$. — Aniruddh Agarwal, Jan 14 '19 at 16:58

score 0 · Answer 1 · answered Jan 14 '19 at 16:58

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Hint: Any root of a polynomial is intricately linked to a linear factor, and polynomials have degrees.

answered Jan 14 '19 at 16:58

Arthur

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Prove that p(x) cannot have more than m zeros , where $p(x)$ is a polynominal of degree m and $p(x) ∈ \mathbb{K} [x]$ and $\mathbb{K}$ is a field

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