Factor the polynomial in quadratic form
x^4-36

Factored
(x^2 +6)(x^2 - 6)
(x^2 + 6)(x + sqrt (6))(x - sqrt (6))

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.