your classmate asserted that x^2 - 4x - 12 and 12 - 4x - x^2 has the same factors is your classmate correct
Factor x^2 - 4x - 12 using binomials:
(x + 2)(x - 6)
Therefore, factors are x = -2, x = 6
Factor 12 - 4x - x^2
-(x - 6)(x + 2)
Therefore, factors are x = -2, x = -6
Because they don't have two matching factors, your classmate is incorrect.
Factor x^2 - 4x - 12 using binomials:
(x + 2)(x - 6)
Therefore, factors are x = -2, x = 6
Factor 12 - 4x - x^2
-(x - 6)(x + 2)
Therefore, factors are x = -2, x = -6
Because they don't have two matching factors, your classmate is incorrect.