From the graph, we can see that the curve cuts the x axis at three points.
At x = 0, x = 2 and x = 5
If x = 0. then x-0 is a factor
If x = 2, then x-2 is a factor
if x = 5, then x-5 is a factor
Multiplying the fac tors together, we will have:
= x(x-2)(x-5)
= (x^2-2x)(x-5)
= x^2(x)-5(x^2)-2x(x)+5(2)
= x^3-5x^2-2x^2+10
= x^3-7x^2+10
The equation of the polynomial graphed is x^3-7x^2+10