Is degree of zero polynomial not defined? If yes why? Can't it be any natural number?
Is degree of zero polynomial not defined? If yes why? Can't it be any natural number?
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)=2x0P(x)=2x0 . P(x) = 100 can be written as100x0100x0. The power of variables is 0. So the degree is 0 in each case. It can’t be written as100x1100x1 or 100x2100x2because the polynomial itself will change as its value and degree will change.
But p(x) = 0 can be written as 0x00x0 or 0x10x1 or 0x20x2 or 0x30x3and 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.
Hope this helps :)
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)=2x0P(x)=2x0 . P(x) = 100 can be written as100x0100x0. The power of variables is 0. So the degree is 0 in each case. It can’t be written as100x1100x1 or 100x2100x2because the polynomial itself will change as its value and degree will change.
But p(x) = 0 can be written as 0x00x0 or 0x10x1 or 0x20x2 or 0x30x3and 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.
Hope this helps :)
