Degree of Polynomial

The sum of the exponents of the variables in a term is called the degree of that term.

For example, the degree of 2x2y is 3 since the sum of the exponents of x and y is 2 + 1, i.e., 3. Similarly, the degree of the term 2x5 is 5.

The degree of a polynomial is the same as the degree of its term or terms having the highest degree and non-zero coefficient.

For example, consider the polynomial

3x4y3 + 7xy5 – 5x3y2 + 6xy

It has terms of degrees 7, 6, 5, and 2 respectively, of which 7 is the highest. Hence, the degree of this polynomial is 7.

A polynomial of degree 2 is also called a quadratic polynomial.

When all the coefficients of variables in the terms of a polynomial are zeros, the polynomial is called a zero polynomial. The degree of a zero polynomial is not defined.