The roots of a polynomial function are the values that give the value zero.
This only happens when one of the factors has a zero value. The product of three non-zero factors will be a non-zero value, but if any of the factors is zero then the product will be zero no matter what the others are.
if x=-1 then (x + 1) = 0
if x = 3, then (x - 3) = 0
if x = ½, then (2x -1) = 0
A polynomial that has these three roots must have these three factors.
(x + 1)(x - 3)(2x - 1) = (x^2 -2x -3)(2x - 1) = 2x^3 -5x^2 - 4x + 3
you can check your work by substituting the roots into the polynomial to confirm that it does indeed have a zero value for those values of x.
