The degree of a nonzero polynomial is the largest exponent of a monomial having nonzero coefficient.
The total degree of a multivariate monomial is . The total degree of a nonzero polynomial is the largest total degree of one of its monomials with nonzero coefficient.
A nonzero polynomial of degree over a field has at most distinct roots. Indeed, each root supplies a linear factor by polynomial division, and induction on gives the bound.
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The degree of a polynomial is defined as the highest power of the variable (often denoted as \(x\)) that appears in the polynomial with a non-zero coefficient. In other words, it is the largest exponent in the polynomial expression.
