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monic definition

Date : 28-02-2023

In mathematics, a polynomial is said to be monic if its leading coefficient (i.e., the coefficient of the term with the highest degree) is 1.

For example, the polynomial x^3 + 2x^2 - 3x + 1 is monic, because the coefficient of the x^3 term is 1, while the polynomial 2x^2 - 3x + 1 is not monic, because the coefficient of the highest-degree term, which is x^2, is 2 instead of 1.

The monic property is often useful in polynomial algebra and factorization, as it allows us to simplify some calculations and make some factorization methods more straightforward.