If x - 2 is a factor of x² - bx + b, where b is a constant. What is the value of b?

Solution:

Given that x - 2 is a factor of x² - bx + b

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

Since x = 2 is a factor, it must satisfy the expression.

According to the remainder theorem, if we substitute x = 2 in the expression x² - bx + b , the result should be 0.

⇒ 22 - 2b + b = 0

⇒ 4 - 2b + b = 0

⇒ 4 - b = 0

⇒ b = 4

The value of b is 4

If x - 2 is a factor of x² - bx + b, where b is a constant. What is the value of b?

Summary:

If x - 2 is a factor of x² - bx + b, where b is a constant then the value of b is 4.