Find a cubic polynomial function having the graph shown Solu

Find a cubic polynomial function having the graph shown.

95 ) graph cuts the x axis at x= -5

zero at x=-5

graph touches the x axis at x = 3

zero at x=3 of multiplicity 2

Polynomial: f(x) = k(x+5)(x -3)^2

We would the constant k by using point (0, 9)

9 = k(5)(-3)^2

k= 1/5

f(x) = (1/5)(x+5)(x -3)^2

f(x) = (x+5)(x^2 +9 -6x)/5

= (x^3 +9x -6x^2 +5x^2 +45 -30x)/5

=(x^3 -x^2 -21x +45)/5