Polynomial ring/Field/One variable/Product of linear factors/Divisors/Exercise

Let ${}K$ be a field, and let ${}K[X]$ be the polynomial ring over ${}K$, and let ${}P\in K[X]$ be a polynomial that has a factorization into linear factors. Let ${}T$ be a divisor of ${}P$. Show that ${}T$ has also a factorization into linear factors, and that the multiplicity of every linear factor ${}X-a$ in ${}T$ is bounded from above by its multiplicity in ${}P$.

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