Các câu c,d sử dụng định lí Bézout nhé
\(c,k\left(x\right)⋮g\left(x\right)\Leftrightarrow3x^3-4x^2-2m=\left(x+1\right)\cdot a\left(x\right)\)
Thay \(x=-1\)
\(\Leftrightarrow3\left(-1\right)^3-4\left(-1\right)^2-2m=0\\ \Leftrightarrow-3-4-2m=0\\ \Leftrightarrow m=-\dfrac{7}{2}\)
\(d,h\left(x\right):g\left(x\right)R\left(-2021\right)\\ \Leftrightarrow-2x^5-2x^4+x^2+mx-3=\left(x+1\right)\cdot b\left(x\right)-2021\)
Thay \(x=-1\)
\(\Leftrightarrow-2\left(-1\right)-2\cdot1+1-m-3=-2021\\ \Leftrightarrow-2-m=-2021\Leftrightarrow m=2019\)
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