In my textbook it indelibly states that f(x)=a, where a cannot equal 0, is a zero degree function. How can that be so? Shouldn't it be a first degree polynomial function, because if it weren't, wouldn't a always be zero then?

Printable View

- Jul 28th 2011, 07:05 AMBashyboyDegree of a polynomial function
In my textbook it indelibly states that f(x)=a, where a cannot equal 0, is a zero degree function. How can that be so? Shouldn't it be a first degree polynomial function, because if it weren't, wouldn't a always be zero then?

- Jul 28th 2011, 07:08 AMSironRe: Degree of a polynomial function
Because you can write:

$\displaystyle f(x)=a=a\cdot 1=a\cdot x^{0}$

So definitely a zero degree polynomial function. - Jul 28th 2011, 07:09 AManonimnystefyRe: Degree of a polynomial function
hi bashyboy

actually when you have a n-th degree polynomial then it means that the maximum exponent of x in that polynomial is n.so if you have a zero degree polynomial than it means that the maximum exponent of x is 0 which means that your polynomial looks ike this:

P(x)=a*x^0

and any number to the power of zero is 1 so:

P(x)=a*1

P(x)=a