Factorisation Of Polynomials

Concept: This problem uses the Factor Theorem. The Factor Theorem states that if is a factor of a polynomial , then . Conversely, if , then is a factor of .

Step 1: Apply the Factor Theorem We are given that is a factor of the polynomial . According to the Factor Theorem, if is a factor, then .

Step 2: Substitute into the polynomial Replace every in with :

Step 3: Simplify the expression for Combine the terms with :

Step 4: Set and solve for Since is a factor, we know . From Step 3, we found . Therefore, we must have: The value of is 0.