Question

 

Answer 1

\(a,f\left(x\right)=x^3+2x^2+ax+2⋮x-2\\ \Leftrightarrow f\left(2\right)=8+8+2a+2=0\\ \Leftrightarrow2a=-18\Leftrightarrow a=-9\\ b,f\left(x\right)=x^4+ax^2+2x-1⋮x+1\\ \Leftrightarrow f\left(-1\right)=1+a-2-1=0\\ \Leftrightarrow a=2\\ c,f\left(x\right)=x^3-3x^2+4x+a⋮x-2\\ \Leftrightarrow f\left(2\right)=8-12+8+a=0\Leftrightarrow a=-4\)

Answer 2

\(10,\\ f\left(x\right)=x^3+2ax^2+bx+2⋮x^2-1=\left(x-1\right)\left(x+1\right)\\ \Leftrightarrow x^3+2ax^2+bx+2=\left(x-1\right)\left(x+1\right)\cdot a\left(x\right)\)

Thay \(x=1\Leftrightarrow1+2a+b+2=0\Leftrightarrow2a+b=-3\)

Thay \(x=-1\Leftrightarrow-1+2a-b+2=0\Leftrightarrow2a-b=-1\)

Từ đó ta đc hệ \(\left\{{}\begin{matrix}2a+b=-3\\2a-b=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-1\\b=-1\end{matrix}\right.\Leftrightarrow a=b=-1\)