a: \(\dfrac{f\left(x\right)}{g\left(x\right)}=\dfrac{2x^4-3x^3+3x-2}{x^2-1}\)
\(=\dfrac{2\left(x^4-1\right)-3x\left(x^2-1\right)}{x^2-1}=2\left(x^2+1\right)-3x\)
b: \(\dfrac{A\left(x\right)}{B\left(x\right)}=\dfrac{2x^3+3x^2-x+m}{2x+1}\)
\(=\dfrac{2x^3+x^2+2x^2+x-2x-1+m+1}{2x+1}\)
\(=x^2+x-1+\dfrac{m+1}{2x+1}\)
Để đây là phép chia hết thì m+1=0
=>m=-1