Find a formula for a cubic function f if

Question

f(3) = 144
and
f(−5) = f(0) = f(4) = 0.

Answer 1

since you have given the three zeroes, it is clear that
f(x) = a(x+5)(x)(x-4)
since f(3) = 144,
a(8)(3)(-1) = 144
a =-6
so
f(x) = -6x(x+5)(x-4)