If x² – x – 6 and x² + 3x – 18 have a common factor (x – a) then find the value of a.

Let f(x) = x² – x – 6 and p(x) = x² + 3x – 18

As (x – a) is the common factor of f(x) and p(x) both, and as by Factor Theorem, we know that,

If p(x) is a polynomial and a is any real number, then g(x) = (x– a) is a factor of p(x), if p(a) = 0 and vice versa.

⇒ f(a) = p (a)

⇒ (a)² – (a) – 6 = (a)² + 3(a) – 18

⇒ 4a = 12

⇒ a = 3

∴ The value of a is 3.