Why is the degree of a zero polynomial not defined?
The degree of zero polynomial is undefined.
Before proceeding further, keep it in mind that: “The degree of the polynomial is the 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, the degree of zero polynomial is undefined.
The degree of zero polynomial is undefined.
Before proceeding further, keep it in mind that: “The degree of the polynomial is the 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, the degree of zero polynomial is undefined.
