Finding out the degree of a polynomial

Given the equation How do we work out the degree and coefficients of it?

Well, the degree is the largest power of X which does not have a coefficient of 0. A coefficient is the number at the front of an element in the polynomial. So would not be okay but would be okay.

Something to note here is that is actually but because 1 * x is just x we don’t include the 1, but it counts in this equation.

So has a degree of 2 (x^2) and has 3 coefficients (starting at 0) So the coefficients are just the number parts.

Some things you need to watch out for:

is not a polynomial because powers of x must be whole numbers.

is not a polynomial because the x’s aren’t combined. It has to be exactly one item per k.

Polynomials defined in terms of functions

Let’s say you have a function such as F(x) = {POLYNOMIAL}. If one of the roots of the polynomial is positive than the output of f(x) is positive. Otherwise it’s always negative.