= Leading coefficient of a polynomial
{title2=$a_n$}
= Leading coefficient
{synonym}
= Leading coefficients of polynomials
{synonym}
The leading coefficient of a nonzero <polynomial> $a_nx^n+\cdots+a_0$, with $a_n\ne0$, 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.
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