SOLUTION

If (t- 8) is a factor of t^2 - kt - 48, then k=

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

\((t - 8)\) is a factor of \(t^2 - kt - 48\) means that \(t = 8\) is a solution of the equation \(t^2 - kt - 48 = 0\).

Substitute\(t = 8\) to get the value of k: \(8^2 - 8k - 48 = 0\) --> \(k = 2\).

Answer: C.
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Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.

If (t- 8) is a factor of \(t^2 - kt - 48\), then k=

(A) - 6
(8) - 2
(C) 2
(0) 6
(E) 14

It is given that \((t - 8)\) is a factor of the quadratic expression \(t^2 - kt - 48\)
Hence, we need to find the other factor of \(-48\) such that the sum of factors is\(-(\frac{-k}{1})=k\).

Thus, \((8) * x = -48\)

Or, \(x = -6\)

So, \(k = 8 + (- 6) = 2\)

Answer: (C)

Since (t - 8) is a factor of t^2 - kt - 48, t = 8 must be a root of the equation t^2 - kt - 48 = 0. We can substitute 8 for t and determine a value for k.

8^2 - 8k - 48 = 0

64 - 8k = 48

-8k = -16

k = 2

Answer: C
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This problem is a good one in a few ways because it has a trap that's useful to learn from and it can be solved in two ways.

The simplest method is to realize that t = 8 is a root of the quadratic (as given), plug it into the equation and solve for k directly.

8^2 - k(8) - 48 = 0
K =2

The other method involves breaking up the quadratic into its roots: (t-8)(t+6) = 0
-Kt = -8t + 6t by FOIL
-k = -2
k = 2

However, it's common to set kt = -2t and thus set oneself up for the trap k = 2, one of the answer choices. So it's important to remember that -kt is an entire term, not just kt itself, so you need to set the entire term = -2t.

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

if we substitute t = 8 in the equation t^2 - kt - 48 , we should get zero.

8*8 -8*t-48 =0

8t = 16

t = 2.

Option C is the answer.

Thanks,

Clifin J Francis,
GMAT SME
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