Answer: [tex]b=4[/tex]
Step-by-step explanation:
The complete exercise is: "If [tex]x-2[/tex] is a factor of [tex]x^2 - bx + b[/tex], where b is a constant, what is the value of b?"
You know that a factor of the given polynomial [tex]x^2 - bx + b[/tex] is:
[tex]x-2[/tex]
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:
[tex]P(x)=x^2 - bx + b[/tex]
2. Now you must substitute [tex]x=2[/tex] into the polynomial:
[tex]P(2)=(2)^2- b(2)+ b[/tex]
3. Since 2 is a zero of the polynomial, you can substitute [tex]P(2)=0[/tex]:
[tex]0=(2)^2- b(2)+ b[/tex]
4. Finally, you must solve for the constant "b" to find its value. Then, this is:
[tex]0=(2)^2- b(2)+ b\\\\0=4-2b+b\\\\-4=-b\\\\b=4[/tex]
