Question

Why is the degree of a zero polynomial is usually 'undefined'?

Answer 1

• Answer:

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. As such, its degree is usually undefined.

Answer 2

Answer:

☞ The degree of zero polynomial is undefined.

Before proceeding further, keep it in mind that: “The degree of the polynomial is highest power of its variable.”

Other constant Polynomials have degree =0. Why is it so? Take for example P(x) = 2. It can be written as P(x)=2x0 . P(x) = 100 can be written as 100x0 . The power of variables is 0. So the degree is 0 in each case. It can’t be written as 100x1 or 100x2 because the polynomial itself will change as its value and degree will change.

But p(x) = 0 can be written as 0x0 or 0x1 or 0x2 or 0x3 and so on. It is so because 0 multiplied by any number will give zero itself as an answer. Now you can see that its degree can be considered as 0,1,2,3 or any other non-negative integer.

Which one to take and which one to reject? This is the reason, degree of zero polynomial is undefined.

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