What is the degree of the polynomial that generates the given points
x: -6 -2 0 2 6
y: -726 -34 0 18 582

You would get a 5th degree polynomial because if you were to set the x coordinates as an equation and multiply them, you'd get:
(x+6)(x+2)(x)(x-2)(x-6)
The x's are opposite of the given coordinates because  you would plug them in like this:
x = 6
x-6 = 6-6
x-6 = 0