\(x^4-x-14=x^4-2x^3+2x^3-4x^2+4x^2-8x+7x-14\)
\(=x^3\left(x-2\right)+2x^2\left(x-2\right)+4x\left(x-2\right)+7\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3+2x^2+4x+7\right)\)
\(\Rightarrow\left(x^4-x-14\right):\left(x-2\right)=\left[\left(x-2\right)\left(x^3+2x^2+4x+7\right)\right]:\left(x-2\right)=x^3+2x^2+4x+7\)