The leading coefficient of a nonzero polynomial
 |
is the coefficient 
of its term of highest degree.
A polynomial whose leading coefficient is 1 is called
monic. Over an ordered
field, namely a field equipped with an ordering compatible
with addition and multiplication, the degree and sign of the leading coefficient
determine the end behavior of a real polynomial.
For a multivariate polynomial, the leading coefficient depends on a chosen monomial order.
It is the coefficient multiplying the leading
monomial, so that 
, where 
is the leading term. For
example, 
over 
has leading coefficient 3 in lexicographic order
with 
and 2 in lexicographic order with 
.
