The real zeros of the polynomial function are
(-2, 0), (-2, 0), (1, 0), (1, 0), (2, 0)
The lease possible degree of the function is 5
How to find the equation
The equation of the polynomial is solved using the formula
f (x) = a (x - p) (x - q) (x - r).....
Where p, q, r, ... are the roots or zeros of the equation
From the graph the zeros are x = -2 twice, x = 1 twice, x = 2
The zeros are the points the graph intersects the x-axis
The points are
(-2, 0), (-2, 0), (1, 0), (1, 0), (2, 0)
The lease possible degree of the function is found from the number of real roots to be 5