Function with zeros 2, -3/2, and -1. Give an equation for the polynomial function.

f(x) =a( x- 2)( x-3/2)(x +1)
= a/2 (x-2)(2x-3)(x+1)
= a/2 (x-2) ( 2x^2 -x -3)
= a/2 ( 2x^3 -x^2 -3x -4x^2 +2x +6)
= a/2 ( 2x^3 - 5x^2 -x +6)
= ax^3 -5a/2 x^2 -a/2 x +3a where a is a real number.

This represents a family of polynomial functions.

f(x) = (x - 2)(x + 3/2)(x + 1)
f(x) = (x^2 - x - 2)(x + 3/2)
f(x) = x^3 + 3/2x^2 - x^2 - 3/2x - 2x - 3
f(x) = x^3 + 1/2x^2 -7/2x - 3

f(x) = (x-2)(2x+3)(x+1) = (2x^2-x-6)(x+1) = 2x^3 + x^2 - 7x - 6