Can the degree of a monomial ever be a negative? please explain why or why not. i will fan and give a medal

Question

anonymous · Answer

@dan815 can you help me please?

matt101 · Answer

The answer is no - the degree of a monomial cannot be negative.

A monomial is defined as a single term containing any combination of constants and non-negative powers of variables (i.e. their exponents are 0 or greater). In fact, a monomial is the simplest example of a polynomial, and polynomials aredefined as expressions composed of constants and variables that are combined using only addition, subtraction, multiplication, and non-negative integer exponents.

As for why that specifically is the definition I can't say for sure as it's beyond my knowledge level, but I would guess it has something to do with the continuity of the function that is produced. For instance, the monomial x^2 is defined at every real value of x. However, x^(-2) is not a monomial, because really you're talking about 1/x^2, where now a discontinuity has been introduced in the form of an asymptote at x=0.

matt101 · Answer

Actually a quick skimming of the Wikipedia article tells me the reason for the definition is somewhat more involved...but all you need to know is that the degree cannot be negative for a monomial.

anonymous · Answer

thank you sooo much you for your help