#math/linear-algebra A number $\lambda \in \mathbf{F}$ is called a `zero` or `root` of a polynomial $p \in \mathcal{P}(\mathbf{F})$ if $p(\lambda)=0$. ## Each Zero Corresponds to a Degree-One Factor Suppose $m$ is a positive integer and $p \in \mathcal{P}(\mathbf{F})$ is a polynomial of degree $m$. Suppose $\lambda \in \mathbf{F}$. Then $p(\lambda)=0$ if and only if there exists a polynomial $q \in \mathcal{P}(\mathbf{F})$ degree $m-1$ such that $ p(z)=(z-\lambda)q(z) $ for every $z\in \mathbf{F}$. ## Degree $\large m$ implies at most $\large m$ zeroes Suppose $m$ is a positive integer and $p \in \mathcal{P}(\mathbf{F})$ is a polynomial of degree $m.$ Then $p$ has at most $m$ zeroes in $\mathbf{F}$.