wordy polynomial question: T/F: in p(x)=(x-x_0)^m * q(x), x_0 is zer of order m

[philip_neri]

True or false: If the number x_0 is a zero of the polynomial p and if there are a number m and a polynomial q(x) such that p(x) = (x-x_0)^m*q(x) with q(x_0) ≠ 0 then we say that x_0 is a zero of the order m.
(underscore denotes subscript)

 

[stapel]

True or false: If the number x_0 is a zero of the polynomial p and if there are a number m and a polynomial q(x) such that p(x) = (x-x_0)^m*q(x) with q(x_0) ≠ 0 then we say that x_0 is a zero of the order m.
(underscore denotes subscript)

What is your book's definition of "a zero of order 'm'"? (And does it allow for m to be just a "number", or must it be a natural number?)

Thank you!