\(x^4+2x^3-16x^2-2x+15=x^4-3x^3+5x^3-15x^2-x^2+3x-5x+15=x^3\left(x-3\right)+5x^2\left(x-3\right)-x\left(x-3\right)-5\left(x-3\right)=\left(x-3\right)\left(x^3+5x^2-x-5\right)=\left(x-3\right)\left[x^2\left(x+5\right)-\left(x+5\right)\right]=\left(x-3\right)\left(x+5\right)\left(x-1\right)\left(x+1\right)\)