Question

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

Answer 1

$\bf x^2-\underline{b} x+b\implies \stackrel{given}{(x-2)}~(x-y)\impliedby \textit{now let's do some FOIL}\\\\ -------------------------------\\\\ \begin{cases} -yx-2x=-\underline{b}x\implies y+2=\underline{b}\\ (-2)(-y)=b\implies 2y=b \end{cases} \\\\\\ \underline{b}=b\implies y+2=2y\implies 2=y$

what is b?   from the first equation in the system, y + 2 = b.