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monic (Definition)

A monic polynomial is a polynomial with a leading coefficient of 1. That is, if $ P_n(x)$ is a polynomial of degree $ n$ in the variable $ x$, then the coefficient of $ x^n$ in $ P_n(x)$ is 1.

For example, $ x^5+3x^3-10x^2+1$ is a monic 5th-degree polynomial. $ 3x^2+2z-5$ is a 2nd-degree polynomial which is not monic.



"monic" is owned by akrowne.
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See Also: Eisenstein criterion, irreducible polynomial, algebraic integer

Other names:  monic polynomial
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Cross-references: coefficient, variable, degree, leading coefficient, polynomial
There are 31 references to this entry.

This is version 6 of monic, born on 2002-02-10, modified 2005-02-28.
Object id is 1899, canonical name is Monic2.
Accessed 9598 times total.

Classification:
AMS MSC: 12E10 (Field theory and polynomials :: General field theory :: Special polynomials)
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