a) \(A=x^2\left(x^2-x+5\right)+\left(x^2-x+5\right)+a-5=\left(x^2-x+5\right)\left(x^2+1\right)+a-5⋮B=\left(x^2-x+5\right)\)
\(\Rightarrow a-5=0\Rightarrow a=5\)
b) \(A=x^2\left(x^2-x-2\right)-8x\left(x^2-x-2\right)+15\left(x^2-x-2\right)-x+ax+30+b\)
\(=\left(x^2-x-2\right)\left(x^2-8x+15\right)-x+ax+30+b⋮B=\left(x^2-x-2\right)\)
\(\Rightarrow\left\{{}\begin{matrix}a=-1\\b=-30\end{matrix}\right.\)
c) \(A=x\left(x^2-2x+3\right)-7\left(x^2-2x+3\right)-4+a=\left(x^2-2x+3\right)\left(x-7\right)-4+a⋮B\)
\(\Rightarrow a=4\)
d) \(A=x^2\left(x^2-6x+5\right)-x\left(x^2-6x+5\right)-\left(x^2-6x+5\right)-x+\left(a-1\right)x+5+b-a\)
\(=\left(x^2-6x+5\right)\left(x^2-x-1\right)-x+\left(a-1\right)x+5+b-a⋮B\)
\(\Rightarrow\left\{{}\begin{matrix}a=0\\b=5\end{matrix}\right.\)
