Chia \(\left(x+3\right)\left(x-4\right)\) chứ ko phải chia \(\left(x+3\right)\left(x+4\right)\) à?
\(P\left(x\right)=\left(x+3\right).Q\left(x\right)+1\) \(\Rightarrow P\left(-3\right)=1\)
\(P\left(x\right)=\left(x+4\right)R\left(x\right)+8\) \(\Rightarrow P\left(-4\right)=8\)
\(P\left(x\right)=\left(x+3\right)\left(x-4\right).3x+ax+b\)
Thay \(x=-3\) vào ta được:
\(P\left(-3\right)=-3a+b\Rightarrow-3a+b=1\)
Thay \(x=-4\) vào ta được:
\(P\left(-4\right)=\left(-4+3\right)\left(-4-4\right).3\left(-4\right)-4a+b\)
\(\Rightarrow-4a+b-96=8\Rightarrow-4a+b=104\)
\(\Rightarrow\left\{{}\begin{matrix}-3a+b=1\\-4a+b=104\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=-103\\b=-308\end{matrix}\right.\)
\(\Rightarrow P\left(x\right)=3x\left(x+3\right)\left(x-4\right)-103x-308\)