<p>(x-8)(x-k) = x^2 - 5kx + m</p>
<p>In the eq. above, k and m are constants. If the eq. is true for all values of x, what is the value of m? Thx</p>
<p>k=2 because -2x + -8x = -10x and -5 * -2 = -10x
Then m equals 16 since -2 * -8.</p>
<p>I don't see any formula rather just doing it in your head I guess.</p>
<p>where'd you get -2x and -8x? and how is -5 * -2 = -10x... wouldn't it be positive? I don't know where you are getting these numbers.. can you actually clarify what you are doing...</p>
<p>I believe the answer is 24</p>
<p>If you expand the first part of the equation, you get x^2 + (-k-8)x + 8k = x^2 -5kx + m. The x^2 cancels out. Then you can see the pattern between the first and second sides of the equation.</p>
<p>-k-8 = -5........therefoe k = 3
8k = m....therefore m = 24</p>
<p>the answer sheet says it is 16</p>
<p>(x-8)(x-k)=x^2-5kx+m</p>
<p>x^2+(-k-8)x+8k=x^2-5kx+m
(-k-8)x+8k=-5kx+m</p>
<p>(-k-8)=-5k
-8=-4k
k=2</p>
<p>(-2-8)x+8(2)=-5(2)x+m
-10x+16=-10x+m
m=16</p>
<p>how did you go from (-k-8)x+8k=-5kx+m to (-k-8)=-5k how did you know m = 8k ?</p>
<p>(x-8)(x-k) = x^2 - 5kx + m
x^2 -kx -8x +8k = x^2 - 5kx + m
x^2 -(k+8)x + 8k = x^2 - 5kx + m --> -kx - 8x becomes -(k+8)x by factoring out the x</p>
<p>In order for the two equations to be equal, the coefficients must be equal.
x^2 = x^2 --> Matches</p>
<p>-(k+8)x = -5kx
-k - 8 = -5k
4k = 8
k = 2 </p>
<p>8k = m
8(2) = m
16 = m</p>
<p>thanks cdn_dancer.. i really appreciate your step by step explanation</p>