x to the power of 10 +5x to the power of 9 +4x to the power of 8 divided by x+2
Do you mean
(x^10 + 5x^9 + 4x^8)/(x+2) ?
If so, then you have
x^8(x^2+5x+4)/(x+2)
x^8(x+1)(x+4)/(x+2)
but I don't see what that has to do with the Binomial Theorem.