\(f\left(x\right):\left(x+1\right)\) dư \(-2\)
\(\Rightarrow f\left(-1\right)=-2\)
\(\Rightarrow-1+a-b+c=-2\)
\(\Rightarrow a-b+c=-1\left(1\right)\)
\(f\left(x\right):\left(x-2\right)\) dư \(7\)
\(\Rightarrow f\left(2\right)=7\)
\(\Rightarrow8+4a+2b+c=7\)
\(\Rightarrow4a+2b+c=-1\left(2\right)\)
\(\left(1\right);\left(2\right)\Rightarrow\left\{{}\begin{matrix}4a+2b+c=-1\\a-b+c=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3a+3b=0\\a-b+c=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b=0\\a-b+c=-1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=-1\\c=-3\end{matrix}\right.\)
\(Q=\left(2024a+2022b+c\right)^{2023}+1\)
\(Q=\left(2024.1+2022.\left(-1\right)-3\right)^{2023}+1=\left(-1\right)^{2023}+1=0\)
