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

Question

jhonyy9 · Answer

given x-2 is a factor of x^2 -bx +b so what mean this ?

silvernight269 · Answer

Wdym

jhonyy9 · Answer

so this mean that you can divide x^2 -bx +b by x-2

do you can make it ?

jhonyy9 · Answer

x^2 -bx +b / x-2 = x +(-b+2) x^2 -2x

-- -bx-(-2x) +b -bx +2x +b (-b+2)x +b (-b+2)x -2(-b+2)

b -(-2(-b+2)) b -(2b-4) b-2b+4 -b+4 so from this result that x^2 -bx +b is divisibly by x-2 than -b+4=0 -b+4=0 b=4 do you understand now the way ?

jhonyy9 · Answer

@ThisGirlPretty

jhonyy9 · Answer

how you think this understandably sure ?

jhonyy9 · Answer

ask me what you dont understood it

sillybilly123 · Answer

If $x-2$ is a factor of $f(x) = x^2-bx+b$, then:

$f(x) = x^2-bx+b = (x - 2) ( x + C)$ ... where $C$ is some [other] number

$\implies f(2) =   (2 - 2) ( 2 + C) = 0 = 2^2 - b(2) + b $

$ \implies b = 4$