Correct Answer - Option 2 : x - 2
Given:
Factor of the x3 + ax + b is,
(x - 1), and (x + 3)
Calculation:
Let,
(x - β) is the remaining factor of the given equation then,
⇒ (x - β)(x - 1)(x + 3) = x3 + ax + b
⇒ (x - β)[x2 + 2x - 3] = x3 + ax + b
⇒ x3 + 2x2 - 3x - βx2 - 2βx + 3β = x3 + ax + b
⇒ x3 + x2(2 - β) - x(3 + 2β) + 3β = x3 + ax + b
On comparing both side,
⇒ 2 - β = 0
β = 2
Hence, the remaining factor is (x - 2)