To find the polynomial function each of the zeros must be transformed into an equation with x and then these are used as factors to find the original polynomial. For x = -4 one add 4 to each side and has x + 4 = 0; for x = 2 one subtracts 2 from each side and has x - 2 = 0; and for x = 3 one subtracts 3 from each side and has x - 3.
Next multiply (x+4) (x-2) (x-3). Multiply two factors together and then the answer by the third. (x+4) (x-2) = x^2 + 2x -8. Then multiply this x^2 + 2x -8.times x - 3. -3 (x^2 + 2x -8.) + x (x^2 + 2x -8.) = -3x^2 -6x + 24 + x^3 + 2x^2 -8x for a total expression of x^3 - x^2 -14x + 24.
