Question

If x + a is a common factor of f(x) = x² + x – 6 and g(x) = x² + 3x – 18, then find the value of a.

Answer 1

Given polynomials are f(x) = x² + x – 6 

and g(x) = x² + 3x – 18 

f(x) and g(x) having common factors 

(x + a), So 

x + a = 0 ⇒ x = -a 

f(-a) = (-a)² + (-a) – 6 

= a² – a – 6 

g(-a) = (-a)² + 3(-a) – 18 

= a² – 3a – 18 

f(-a) = g(-a) 

a² – a – 6 = a² – 3a – 18 

a² – a² – a + 3a = -18 + 6 

2a = -12 

a = -6.