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For what values of the \(\alpha \) parameter, the polynomial
\(W(x)=x^3-(2 \sin4\alpha)x^2+3x-\sin4\alpha-5\)
is divisible by the binomial \((x-2)\)?

Sorry for writing it down, but I didn't know how else to do it.

\[(x-2)\mid w(x)\iff w(2)=0\\
2^3-(2 \sin4\alpha)\cdot2^2+3\cdot2-\sin4\alpha-5=0\\
\sin4\alpha=1\\
\alpha={\pi\over8}+k\cdot{\pi\over2}\wedge k\in\zz\]
I greet You

[edited] poprawa postu, janusz55: dziękuję za zwrócenie uwagi!