這條怎計? Given that F(x)=x^3 - 2x^2 - 5x +6 (a) Show that x+2 is the factor of F(x). (b) Hence, factorize F(x).?

(a)
F(x) = x³ - 2x² - 5x + 6
Consider F(-2) = -8 - 2(4) - 5(-2) + 6 = -16 + 10 + 6 = 0
By factor theorem, x + 2 is a factor of F(x).

(b)
F(x)
= x³ - 2x² - 5x + 6
= x³ + 2x² - 4x² - 5x + 6
= x³ + 2x² - 4x² - 8x + 3x + 6
= x²(x + 2) - 4x(x + 2) + 3(x + 2)
= (x + 2)(x² - 4x + 3)　＜－－　or you can achieve this step by long division
= (x + 2)(x - 1)(x - 3)