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Leading Coefficient

The leading coefficient of a nonzero polynomial

p(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_0 with a_n!=0

is the coefficient a_n 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.

See also

Coefficient, Monic Polynomial, Ordered Field, Polynomial Degree, Real Polynomial

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References

Lang, S. Algebra, 3rd ed. New York: Springer-Verlag, 2002.

Cite this as:

Weisstein, Eric W. "Leading Coefficient." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LeadingCoefficient.html

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