In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

⇒ ax² +a²x + x + a =0

⇒ ax(x + a) + 1(x + a) = 0

⇒ (ax + 1)(x + a) = 0

⇒ x = -a, -1/a