Posted by Lisa on .
(x8)(xk) = x^25kx+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?

SAT algebra 
Reiny,
(x8)(xk) = x^25kx+m
x^2  kx  8x + 8k = x^2  5kx + m
x^2  x(k + 8) + 8k = x^2  5kx + m
for the equation to be true
x(k+8) = 5kx and 8k = m
k+8 = 5k and m = 8k
6k =8
k = 4/3
then m = 8(4/3) = 32/3 
SAT algebra 
Anonymous,
x(k+8)=5kx then why not k+8=5k => k=2 and m=16. why it is k+8=5k. thought answere was 16. I did not have ansewer choice of 32/3 in the book.

SAT algebra 
anon,
yeah, don't pay attention to original answerer... they are totally wrong.
i'm looking for help too : 
SAT algebra 
janae,
Reiny was right until 4th line up from the bottom. when you divide x out, the equation should read k+8=+5k, not negative. thus, k would become 2, not 4/3 which leads us to m= 16

SAT algebra 
Francis NtiFrimpong,
x^2 x(k+8)+8k=x^25kx+m
let x(k+8) equivalent to 5kx & let 8k equivalent to m...
(x(k+8))/x=(5kx)x
x crosses out so
k+8=5k....
8=5kk
8=4k
2=k
if 8k=m then 8(2)=m
16=m