Question

Factorise and solve : x^3-x^2-4x+4

Answer 1

(x - 1)(x - 2)(x + 2)

note that the sum of the coefficients 1 - 1 - 4 + 4 = 0

thus x = 1 is a root and (x - 1 ) is a factor

dividing x³ - x² - 4x + 4 by (x - 1)

x³ - x² - 4x + 4 = (x - 1)(x² - 4 ) (note (x² - 4 ) is a difference of squares )

x³ - x² - 4x + 4 = (x - 1)(x - 2)(x + 2)

(x - 1)(x - 2)(x + 2 ) =0

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = - 2

solutions are x = 1 or x = ± 2