Leading coefficient of a polynomial ($a_n$)

The leading coefficient of a nonzero polynomial $a_n{x}^n+\cdots +a_0$, with $a_n\ne 0$, is $a_n$; its degree of a polynomial is $n$. A monic polynomial has leading coefficient one. For polynomials over a field, a product has leading coefficient equal to the product of the two leading coefficients, which prevents cancellation of their highest-degree terms.