I think you are wrong in the number of even and odd numbers in English

even numbers: số chẵn odd numbers: số lẻ

So in this post must be n is a odd number.

\(n^4-10n^2+9=n^4-n^2-9n^2+9=n^2\left(n^2-1\right)-9\left(n^2-1\right)=\left(n^2-1\right)\left(n^2-9\right)=\left(n-1\right)\left(n+1\right)\left(n-3\right)\left(n+3\right)\)

Because n is a odd number so we can write n at the form n = 2k+1

So \(\left(n-1\right)\left(n+1\right)\left(n-3\right)\left(n+3\right)=\left(2k+1-1\right)\left(2k+1+1\right)\left(2k+1-3\right)\left(2k+1+3\right)\)

\(=2k\left(2k+2\right)\left(2k-2\right)\left(2k+4\right)=2k\cdot2\left(k+1\right)\cdot2\left(k-1\right)\cdot2\left(k+2\right)=16\left(k-1\right)k\left(k+1\right)\left(k+2\right)⋮16\)

But (k-1)k(k+1)(k+2) is the product of four consecutive integers so has multiples of 2,3,4 so \(⋮\left(2\cdot3\cdot4\right)=24\)

So \(n^4-10n^2+9⋮\left(16.24\right)=384\)