What is the value of the leading coefficient a if the polynomial function P(x) = a(x + b)2(x − c) has multiplicity of 2 at the point (−1, 0)

P(x)  =  a(x + b)²(x - c)

 

point (-1, 0) is a zero with multiplicity 2   --->   b = 1

point (4, 0) is on the graph   --->  c = 4

 

P(x)  =  a(x + 1)²(x - 4)

 

contains the point (0, -12)   --->   -12  =  a(0 + 1)²(0 - 4)

                                                     -12  =  a(1)(-4)

                                                        3  =  a