\(A:B=\left(3x^4+3x^2+x^3+x-3x^2-3+5x+8\right):\left(x^2+1\right)\\ =\left[3x^2\left(x^2+1\right)+x\left(x^2+1\right)-3\left(x^2+1\right)+5x+8\right]:\left(x^2+1\right)\\ =3x^2+x-3\left(\text{dư }5x+8\right)\\ \text{Vậy }A=\left(x^2+1\right)\left(3x^2+x-3\right)+5x+8\)