https://diendan.hocmai.vn/threads/toan-8-chung-minh-chia-het.292084/

[toán 8] chứng minh chia hết | - Thím Hải 

b, ta có

8\((x)^{9}\)-\(9(x)^{8} +1 \)= (8x^9 -8x^8)-(x^8-1)

=8x^8(x-1)-(x-1)(x^7+x^6+x^5+...+x+1)

=(x-1)(8x^8-x^7-x^6-......-x-1)

=(x-1)[(x^8-x^7)+(x^8-x^6)+.....+(x^8-1)]

=(x-1)[x^7(x-1)+ x^6(x^2-1)+.......+(x-1).(x^7+x^6+.....+x+1)]

=(x-1)^2.[x^7+x^6(x+1)+x^5(x^2+x+1)+.....+(x^7+x^6+...+x+1)]

\(\Rightarrow\) C chia hết cho D(dpcm)

c) Đặt \(f\left(x\right)=x^{10}-10x+9\)

Giả sử \(f\left(x\right)⋮\left(x-1\right)^2\)

\(\Rightarrow f\left(x\right)=\left(x-1\right)^2Q\left(x\right)\)

\(\Leftrightarrow f\left(1\right)=\left(1-1\right)^2Q\left(1\right)\)

                  \(=0\)

\(\Leftrightarrow1^{10}-10.1+9=0\)

\(\Leftrightarrow0=0\)( đúng)

\(\Rightarrow\)điều giả sử đúng

\(\Rightarrow f\left(x\right)⋮\left(x-1\right)^2\left(đpcm\right)\)