For roots of -2, 5, and 7.
x = -2, x = 5, and x = 7
x = -2 x = 5 x = 7
(x + 2) = 0 (x - 5) = 0 (x - 7) = 0
The polynomial of least degree would be:
(x -2)(x - 5)(x - 7) = 0
(x -2)(x -5) = x(x - 5) - 2(x -5)
= x² - 5x - 2x + 10
= x² - 7x + 10
(x² - 7x + 10)(x -7)
x(x² - 7x + 10) - 7(x² - 7x + 10)
x³ - 7x² + 10x - 7x² + 49x - 70
x³ - 7x² - 7x² + 10x + 49x - 70
x³ - 14x² + 59x - 70
The least is x³ - 14x² + 59x - 70