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`

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`