A math question for the new PSATs,
If x-2 is a factor of x^2 – bx + b, where b is a constant, what is the value of b?
From what you’re given, you know that , for some constant a. From that, you know that –2 + a = –b, and that –2a = b.
Multiply that second equation by –1, and then you can do some solvin’.
–2 + a = –b
2a = –b
–2 + a = 2a
–2 = a
Confirm that works by FOILing:
Yep, that works!
So that’s the algebraic solution. I suspect that once you’ve seen a few questions like this, you might be able to see it without doing the algebra.