\(a,\Leftrightarrow x^4+ax^2-2x+5=\left(x-1\right)\cdot a\left(x\right)+7\)
Thay \(x=1\Leftrightarrow1+a-2+5=7\Leftrightarrow a=3\)
\(b,\Leftrightarrow2x^5-x^4+ax^3-4x^2+x-2=\left(x+1\right)\cdot b\left(x\right)+6\)
Thay \(x=-1\Leftrightarrow-2-1-a-4-1-2=6\Leftrightarrow a=-16\)
\(c,\Leftrightarrow x^{10}+ax^3+b=\left(x^2-1\right)\cdot c\left(x\right)+2x+1\\ \Leftrightarrow x^{10}+ax^3+b=\left(x-1\right)\left(x+1\right)\cdot c\left(x\right)+2x+1\)
Thay \(x=1\Leftrightarrow a+b+1=3\Leftrightarrow a+b=2\left(1\right)\)
Thay \(x=-1\Leftrightarrow1-a+b=-1\Leftrightarrow a-b=2\left(2\right)\)
Từ \(\left(1\right)\left(2\right)\Leftrightarrow\left\{{}\begin{matrix}a=2\\b=0\end{matrix}\right.\)
\(d,\Leftrightarrow x^4-x^3-3x^2+ax+b=\left(x-2\right)\left(x+1\right)\cdot d\left(x\right)+2x-3\)
Thay \(x=2\Leftrightarrow16-8-12+2a+b=1\Leftrightarrow2a+b=5\left(1\right)\)
Thay \(x=-1\Leftrightarrow1+1-3-a+b=-5\Leftrightarrow a-b=4\left(2\right)\)
\(\left(1\right)\left(2\right)\Leftrightarrow\left\{{}\begin{matrix}a=3\\b=-1\end{matrix}\right.\)
