<p>Practice Test #3 in the BB, Section 5 #8</p>
<p>(x-8)(x-k) = x^2-5kx+m</p>
<p>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?</p>
<p>m=16</p>
<p>x^2 - kx - 8x + 8k = x^2 - 5kx + m
8k - kx - 8x = -5kx + m</p>
<p>-kx - 8x = (-5k)x
(-k-8)x = (-5k)x
-k - 8 = - 5k
k = 2</p>
<p>8k = m
8 * 2 = m
m = 16</p>
<p>the easier way:
First factor the equation:
x^2 -kx-8x+8k
Then set the two middle terms (the ones with only one x) equal to eachother:
kx-8x=-5kx
Then plug in any value for x (I would use 1 because that’s the easiest)
k-8=5k
Solve for k
k=2</p>
<p>Then you can set the final terms (the constants, that have no x, equal to eachother)
8k=m
Finally, plug in k
m=16</p>