P(x) = a(x + b)2(x - c)
P(x) = a(x + b)(x + b)(x - c) Multiplied out.....
P(x) = ax3 - acx2 + 2abx2 - 2abcx + ab2x - ab2c So P(x) does have a degree of 3 .
P(x) has multiplicity of 2 at (-3, 0) and passes through (2, 0) so...
P(x) = a(x + 3)2(x - 2)
P(x) passes through (0, 36) so P(0) = 36
P(0) = a(0 + 3)2(0 - 2)
36 = a(0 + 3)2(0 - 2)
36 = a(9)(-2)
36 = -18a
a = -2
Here's a graph: https://www.desmos.com/calculator/ic91u5dxbl