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

Step-by-step explanation:

Factor

x^2-6x+8<0

(x-2)(x-4)<0

For this to be less than zero the factors must have opposite signs.

x>2 and x<4

2<x<4

So x is all real numbers between 2 and 4 or in interval notation

x=(2,4)