Factorisation

Step 1: Understanding the factor theorem The factor theorem states: If is a factor of a polynomial , then . This means the value that makes the factor zero is a root of the polynomial.

Step 2: Rewriting the given factor In this question, the factor is , which can be written as . So, comparing with the factor theorem form, we get: .

Step 3: Applying the factor theorem Since , we substitute into the function to check if it's a root: If is a factor, then

Step 4: Final conclusion Hence, for to be a factor of , it must satisfy .

The correct option is (B):