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by Brent@GMATPrepNow » Thu Nov 01, 2012 7:58 am
granite wrote:If (t-8) is a factor of t^2 - kt - 48, then k =

A -6
B -2
C 2
D 6
E 14

OA C
If (t-8) is a factor then we know that (t-8)(something) = t^2 - kt - 48
Change this to: (t-8)(t+n) = t^2 - kt - 48
We can see that (-8)(n) = -48
So, n must equal 6
So, we now know that: (t-8)(t+6) = t^2 - kt - 48
Expand the left side to get: t^2 - 2t - 48 = t^2 - kt - 48
So, k must equal 2

Answer = C

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by granite » Thu Nov 01, 2012 8:08 am
Brent - I'm confused about how to get to (-8)(n) = -48. What happened to the -kt?

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by Brent@GMATPrepNow » Thu Nov 01, 2012 8:27 am
granite wrote:Brent - I'm confused about how to get to (-8)(n) = -48. What happened to the -kt?
To answer that, let's make some observations about what happens when we multiply 2 binomials.
Some examples:
(x + 3)(x + 2) = x^2 + 5x + 6 (notice that 3 times 2 = 6)
(x + 5)(x - 3) = x^2 + 2x - 15 (notice that 5 times -3 = -15)
(x -2)(x - 7) = x^2 - 9x + 14 (notice that -2 times -7 = 14)

So, if we know that (t - 8)(t + n) = t^2 - kt - 48, then we can conclude that -8 times n = -48

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by granite » Thu Nov 01, 2012 8:56 am
That makes sense now.

The book's (GMAT Quantitative Review, 2nd edition) explanation didn't make sense to me:

If (t-8) is a factor of the expression t^2 - kt - 48, then t = 8 is a solution of the equation t^2 - kt - 48 = 0. So,

8^2 - 8k - 48 = 0
64 - 8k - 48 = 0
16 - 8k = 0
16 = 8k
2 = k