Rational Polynomial is Content Times Primitive Polynomial

Theorem
Let $\Q \sqbrk X$ be the ring of polynomial forms over the field of rational numbers in the indeterminate $X$.

Let $\map f X \in \Q \sqbrk X$.

Then:
 * $\map f X = \cont f \, \map {f^*} X$

where:
 * $\cont f$ is the content of $\map f X$
 * $\map {f^*} X$ is a primitive polynomial.

For a given polynomial $\map f X$, both $\cont f$ and $\map {f^*} X$ are unique.