Degree of A Polynomial - The Degree of The Zero Polynomial

The Degree of The Zero Polynomial

Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial. It has no nonzero terms, and so, strictly speaking, it has no degree either. The above rules for the degree of sums and products of polynomials do not apply if any of the polynomials involved is the zero polynomial.

It is convenient, however, to define the degree of the zero polynomial to be minus infinity, −∞, and introduce the rules

and

For example:

• The degree of the sum is 3. Note that .
• The degree of the difference is . Note that .
• The degree of the product is .

The price to be paid for saving the rules for computing the degree of sums and products of polynomials is that the general rule

breaks down when .