Question

Find a third degree polynomial P(x) that has zeros at x=-1, x=1, x=2 and whose x-term has coefficient 3?

Answer 1

P(x) = a(x+1)(x-1)(x-2)
= ax^3 - 2ax^2 - ax + 2a

Looks like a = -3

P(x) = -3(x+1)(x-1)(x-2) = -3x^3 + 6x^2 + 3x - 6