A polynomial that could be represented by this graph is P(x) = (x + 2)(x - 1)(x - 3).
Based on the information provided about this polynomial function, we can logically deduce that it has a root of multiplicity 1 at x = -2 multiplicity 1 at x = 3, and zero of multiplicity at x = 1;
x = 2 ⇒ x + 2 = 0.
(x + 2)
x = 1 ⇒ x - 1 = 0.
(x - 1)
x = 3 ⇒ x - 3 = 0.
(x - 3)
In this context, an exact equation that represent the polynomial function is given by:
P(x) = a(x + 2)(x - 1)(x - 3)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 6), we have the following;
6 = a(0 + 2)(0 - 1)(0 - 3)
6 = 6a
a = 6/6
a = 1
Therefore, the required polynomial function in factored form is given by:
P(x) = (x + 2)(x - 1)(x - 3)