Give the simplest possible equation for this graph Fx Soluti

Give the simplest possible equation for this graph F(x)=

Solution

Zeros are at x = -2 , 0 and 3

Multiplicity if x = -2 is : 1
Mult of x = 0 is 2
Mult of x = 3 is : 1

For zero = -2, factor is x + 2

For zero = 0 with multiplicity of 2, we have x^2

For zero = 3 with mult = 1, we have x - 3

So, simplest possible equation is :
(x + 2)^1 * (x)^2 * (x - 3)^1

So, the function is :

x^2(x + 2)(x - 3) ----> ANSWER