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I'm preparing for the SAT and tripped over the following problem:

$(x-8)(x-k) = x^2 - 5kx + m$

"In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m? A) 8 B) 16 C) 24 D) 32 E) 40 " Can someone please explain how to solve it?

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Open $(x-8)(x-k) and compare its values with RHS – Rohinb97 Jun 4 '14 at 15:12
Expand the L.H.S., compare co-efficients of like powers of $x$ on both sides and then solve for $k$ and $m$. – Indrayudh Roy Jun 4 '14 at 15:12
up vote 4 down vote accepted

$(x-8)(x-k) = x^2 - (k+8)x + 8k = x^2 - 5kx + m$. Thus:

$k + 8 = 5k$, and $m = 8k$.

So: $k = 2$, and $m = 16$

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Thanks for the response. What I wonder is why I cannot get to something meaningful when I reach x = (m-8k) / (4k - 8) – user1113314 Jun 4 '14 at 15:43

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