What are the simplest factors of this polynomial? x3 + 4x2 – 9x – 36

1. Factor out  common terms in the first two terms, then in the last two terms:
x^2(x + 4) - 9(x + 4)
2. Factor out the common term x + 4
(x + 4)(x^2 - 9)
3. Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3
(x + 4)(x^2 - 3^2)
4. Use Difference of Squares: a^2 - b^2 = (a + b)(a - b)
(x + 4)(x + 3)(x - 3)

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.