# Finding out the degree of a polynomial

Given the equation $x^2 - 3x + 2$ 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 $0^6$ would not be okay but $1^6$ would be okay.

Something to note here is that $x^2$ is actually $1x^2$ but because 1 * x is just x we don’t include the 1, but it counts in this equation.

So $x^2 - 3x + 2$ has a degree of 2 (x^2) and has 3 coefficients (starting at 0) $c_2 = 1, c_1 = 3, c_0 = 2$ So the coefficients are just the number parts.

Some things you need to watch out for:

$x^-1 + x + 1$ is not a polynomial because powers of x must be whole numbers.

$x^2 + x^2 + x + x + 1$ is not a polynomial because the x’s aren’t combined. $x^2+x^2 = x^4$ 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.