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Ta có: \(\left\{{}\begin{matrix}f\left(5\right)=125a+25b+5c+2021\\f\left(4\right)=64a+16b+4c+2021\end{matrix}\right.\)
\(f\left(5\right)-f\left(4\right)=2020\) \(\Rightarrow61a+9b+c=2020\)
Ta có: \(\left\{{}\begin{matrix}f\left(7\right)=343a+49b+7b+2021\\f\left(2\right)=8a+4b+2c+2021\end{matrix}\right.\)
\(\Rightarrow f\left(7\right)-f\left(2\right)=335a+45b+5b=5\left(61a+9b+c\right)=5.2020\)
\(\Rightarrow f\left(7\right)-f\left(2\right)\) chia hết cho 5 nên nó là hợp số.
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: x=100
\(\Leftrightarrow x+1=101\)
Ta có: \(f\left(x\right)=x^{10}-101x^9+101x^8-101x^7+...+101x+2021\)
\(=x^{10}-x^9\cdot\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x\left(x+1\right)+2021\)
\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^2+x+2021\)
\(=x+2021\)
\(=100+2021=2121\)
có ai biết làm ko