Test 3 Section 5 - #8 (page 527)

You can BACKSOLVE this one.  Start with (C), which says m = 24.  If that's true, then:

(x - 8)(x - k) = x² - 5kx + 24

You know from all the factoring/FOILing you've ever done in school that k has to be 3, because (-8)(-3) = 24.  But does that work with the rest of the equation?  Test, substituting 3 in for k: 

(x - 8)(x - 3) = x² - 5(3)x + 24

x² - 11x + 24 = x² - 15x + 24

EEK!  When you FOIL out the left hand side, it doesn't work!

So do the same process now, using (B)* instead, which says x = 16:

(x - 8)(x - k) = x² - 5kx + 16

Using the same logic we just used above, we know k has to be 2, since (-8)(-2) = 16.  Test it, using 2 for k:

(x - 8)(x - 2) = x² - 5(2)x + 16

x² - 10x + 16 = x² - 10x + 16

Everything matches up this time!  (B) must be our answer!

* How do we know to try (B) next instead of (D), you ask?  Well, basically looking at how -5(3) = 15 was BIGGER than -8 - 3 = -11, and realizing that those numbers are only going to get further away from each other if our answer gets bigger.  This is a bit persnickety to explain, but the good news is if you try (D), you'll see very quickly that it didn't work and you got further away, so you'll know to try (B) next.