So since -2, 0, 1 are the roots:
Therefore x = -2, x = 0 , x = 1
Implies that:
x = 2 x - 2 = 0
x = 0 x = 0
x = 1 x - 1 = 0
Therefore (x - 2)x(x - 1) = 0
(x - 2)(x - 1) = x(x - 1) - 2(x - 1) = x² - x - 2x + 2 = x² - 3x + 2
(x - 2)x(x - 1) = 0
(x - 2)(x - 1)x = 0
(x² - 3x + 2)x = 0
x*x² - x*3x + x*2 = 0
x³ - 3x² + 2x = 0
This is the polynomial with the least degree, because it possible for another polynomial with higher power to still have the same root.
x³ - 3x² + 2x = 0 is the polynomial.
I hope this helps.
