# If x - 2 is a factor of x^{2} - bx + b, where b is a constant, what is the value of b?

We will use the concept of the remainder theorem to find the required value of b.

## Answer : If x - 2 is a factor of x^{2} - bx + b, where b is a constant, then b = 4.

Let us see how we will use the concept of the remainder theorem to find the required value of b.

**Explanation:**

According to remainder theorem if x^{2} + bx + c is divided by (x - d) then on substituting x = d in x^{2} + bx + c we get the required remainder.

It is given that (x - 2) is the factor of x^{2} - bx + b . If we substitute x = 2 in the expression x^{2} - bx + b , the result should be 0.

Hence , on substituing x = 2 and equating the expression to 0 we get,

4 - 2b + b = 0

4 - b = 0

b = 4