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 + a – a²x – x = 0

⇒ ax² – x(a² + 1) + a = 0

⇒ ax(x – a) – 1(x – a) = 0

⇒ (ax – 1)(x – a) = 0

⇒ x = 1/a, a