Write the polynomial of least degree with roots -2, 5, and 7.

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

31 is prime. and it’s prime factorization is just 31.