Đặt \(P\left(x\right)=a^2x^3+3ax^2-6x-2a\)
Để \(P\left(x\right)⋮x+1\Leftrightarrow P\left(-1\right)=0\)
\(\Leftrightarrow P\left(-1\right)=-a^2+3a+6-2a=0\)
\(\Leftrightarrow-a^2+a+6=0\)
\(\Leftrightarrow-a^2+3a-2a+6=0\)
\(\Leftrightarrow-a\left(a-3\right)-2\left(a-3\right)=0\)
\(\Leftrightarrow\left(a-3\right)\left(-a-2\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}a-3=0\\-a-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=3\\a=-2\end{matrix}\right.\)
Vậy....
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