Given that 𝑓(𝑥) is a cubic function with zeros at −9, −1, and 6, find an equation for 𝑓(𝑥) given that 𝑓(10)=9.

Answer 1

f(x) = (x+9)(x+1)(x-6) has zeroes -9, -1 and 6

f(10) = (10+9)(9+1)(9-6) = 19(10)(3) = 570 which could be made into 9 by multiplying by 9/570 = 3/190

f(x) = (3/190)(x+9)(x+1)(x-6) is the equation with the requisite zeroes and where f(10) = 9

You can multiply it all out, if you prefer, to get a 3rd degree polynomial, with fractional coefficients and 4 terms.