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**Ant** Let $\displaystyle P(z)$ be a polynomial. We're trying to show that we can write:

$\displaystyle P(z)=c(z-z_1)^{m_1}(z-z_2)^{m_2}...(z-z_{m_k})^{m_k}$.

If $\displaystyle P(z)$ has a root $\displaystyle z_1$ (and it does by the FTA) then we can write:

$\displaystyle P(z)=(z-z_1)^{m_1}P_1(z)$ for some entire function $\displaystyle P_1(z)$.

Next, in my notes it says "Clearly, $\displaystyle |P_1(z) \leq C(|z|+1)^n $

I really don't see how that is "clear", could anyone help?

Thanks.