Find an expression for a cubic function f if f5 80 and f3

Find an expression for a cubic function f if f(5) = 80 and f(3) = f(0) = f(6) = 0.

f(-2) = f(0) = f(6) = 0

So, we have factors (x - (-2)), i.e (x+2)

(x - 0) --> x

and

x - 6

So, the function is of the form :

y = a(x + 3)(x)(x - 6)

Now, f(5) = 80, which is what we use to find the value of constant a :

80 = a(5 + 3)(5(5 - 6)

80 = a(8)(5)(-1)

a = -2

So, the function is :

y = -2(x + 3)(x)(x - 6)

Multiply it out :

y = (-2x - 6)(x^2 - 6x)

y = -2x^3 + 12x^2 - 6x^2 + 36x

Combining like terms :

y = -2x^3 + 6x^2 + 36x ----> ANSWER