Degree of a Polynomial

goldtx
Tue, 18 Jul 2006 13:06:07 +0000

Just so you don’t get confused easily, always keep in mind that polynomials must have the following form:

f(x) = a(sub n) x(sub n) + a(sub n-1) x(sub n-1) + … + a(sub 1) x + a(sub 0)

where n must be a non-negative integer (i.e., a whole number or zero). The coefficients a(sub n), a(sub n-1), …, a(sub 1), a(sub 0) must be real numbers.

The degree of the polynomial function is the highest value of n where a(sub n) is not zero.

Using the above as a guideline, we can quickly tell that:

A is a polynomial with a degree of 4.

B is not a polynomial since - 5 sqrt(x) equals to -5 x^(1/2), and (1/2) is not an integer.

C is technically a polynomial with a degree of 0.

D is not a polynomial since its form does not follow the general form given above.