Question

X2-x-6 and x2+3x-18 have common factor x-a find value of a

Answer 1

X2-x-6=X2+3x-18 (when x=a by factor theorem)
So,
A2-A-6=A2+3A-18
4A=12
A=3

Answer 2

a2-a-6       ; -6= -3*2
a2-3a+2a-6
a(a-3)+2(a-3)
a=3 or -2

a2+3a-18              ;-18= -3 * 6
a2-3a+6a-18
a(a-3)+6(a-3)
a=3 or -6

common factor = x = a = 3