Find the GCD of the following

x² – x – 2,x² + x – 6,3x² – 13x + 14

Given,

x² – x – 2 = x² – 2x + x – 2 = x(x – 2) + 1(x – 2) = (x + 1)(x – 2)

x² + x – 6 = x² + 3x – 2x – 6

= x(x + 3) – 2(x + 3) = (x – 2)(x + 3)

3x² – 13x + 14 = 3x² – 6x – 7x + 14 = 3x(x – 2) – 7(x – 2)

= (x – 2)(3x – 7)

Greatest common divisor = (x – 2)