Hey Mike,

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?Thanks,

Brian.

From what you’re given, you know that , for some constant *a*. From that, you know that –2 + *a* = *–b*, and that –2*a* = *b*.

Multiply that second equation by –1, and then you can do some solvin’.

–2 + *a* = –*b
*2

*a*= –

*b*

–2 + *a* = 2*a
*–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.