<p>Math Problem Help 2nd Edition BB</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>A. 8
B. 16
C. 24
D. 32
E. 40</p>
<p>Thanks</p>
<p>(x-8)(x-k) = x^2 -5kx +m</p>
<p>x^2-kx-8x+8k= x^2-5kx+m</p>
<p>-kx-8x+8k= -5kx+m
let x be 0(since its true for all values)</p>
<p>8k=m</p>
<p>Solve m for the value of k
-kx-8k+8k= -5kx + 8k(which was previously m)
-kx-8k= -5kx
-k − 8 = -5k
-8 = -4k
k = 2</p>
<p>Substitute that value into the other equation:
m = 8k
m = 8(2) = 16</p>