\(p\left(x\right)=x^4+ax^2+bx+c=\left(x^3-3x^2+3x-1\right)\left(x+3\right)+\left(a+6\right)x^2+\left(b-8\right)x+\left(c+3\right)=\left(x-1\right)^3\left(x+3\right)+\left(a+6\right)x^2+\left(b-8\right)x+\left(c+3\right)\).
Do đó: \(\left(a+6\right)x^2+\left(b-8\right)x+\left(c+3\right)⋮\left(x-1\right)^3\Leftrightarrow a=-6;b=8;c=-3\).