Đáp án:
$ A=\dfrac{x^{11}+2005x^{10}+2006}{x+1}$
Giải thích các bước giải:
$A=x^{10}-2006x^9+2006x^8-2006x^7+2006x^6+...-2006x+2006$
$\rightarrow A=(2006x^{10}-2006x^9+2006x^8-2006x^7+2006x^6+...-2006x+2006)-2005x^{10}$
$\rightarrow A=2006(x^{10}-x^9+x^8-x^7+x^6+...-x+1)-2005x^{10}$
$\rightarrow A=2006\dfrac{x^{11}+1}{x+1}-2005x^{10}$
$\rightarrow A=\dfrac{2006x^{11}+2006-2005x^{10}.(x+1)}{x+1}$
$\rightarrow A=\dfrac{2006x^{11}+2006-2005x^{11}-2005x^{10}}{x+1}$
$\rightarrow A=\dfrac{x^{11}+2005x^{10}+2006}{x+1}$
