Question

17 If x-2 is a factor of x- bx + b, where b is a constant, what is the value of b ?

Answer 1

Answer: $b=4$

Step-by-step explanation:

The complete exercise is: "If $x-2$ is a factor of $x^2 - bx + b$, where b is a constant, what is the value of b?"

You know that a factor of the given polynomial $x^2 - bx + b$ is:

$x-2$

Then, in order to find the value of "b", which is a constant of the polynomial, you need to follow these steps:

1. You must rewrite the polynomial as:

$P(x)=x^2 - bx + b$

2. Now you must substitute $x=2$ into the polynomial:

$P(2)=(2)^2- b(2)+ b$

3. Since 2 is a zero of the polynomial, you can substitute $P(2)=0$:

 $0=(2)^2- b(2)+ b$

4. Finally, you must solve for the constant "b" to find its value. Then, this is:

$0=(2)^2- b(2)+ b\\\\0=4-2b+b\\\\-4=-b\\\\b=4$