a, x^4-2x^3-9x^2+16x-6=x^4+2x^3-3x^2-4x^3-8x^2+12x+2x^2+4x-6 =x^2(x^2+2x-3)-4x(x^2+2x-3)+2(x^2+2x-3) =(x^2+2x-3)(x^2-4x+2) =(x-1)(x+3)(x^2-4x+2)b, x^4-6x^3+7x^2+2x-3=x^4-x^3-x^2+5x^3+5x^2+5x+3x^2-3x-3 =x^2(x^2-x-1)-5x(x^2-x-1)+3(x^2-x-1) =(x^2-x-1)(x^2-4x-4)c, x^4+x^3-27x^2-8x+12=x^4+5x^3-3x^2-4x^2+20x^2+12x-4x^2-20x+12 =x^2(x^2+5x-3)-4x(x^2+5x-3)-4(x^2+5x-3) =(x^2+5x-3)(x^2-4x-4)d, x^3-6x^2+11x-6=x^2-3x^2-3x^2+9x+2x-6 =x^2(x-3)-3x(x-3)+2(x-3) =(x-3)(x^2-3x+2) =(x-3)x^2-x-2x+2)
a, x^4-2x^3-9x^2+16x-6=x^4+2x^3-3x^2-4x^3-8x^2+12x+2x^2+4x-6 =x^2(x^2+2x-3)-4x(x^2+2x-3)+2(x^2+2x-3) =(x^2+2x-3)(x^2-4x+2) =(x-1)(x+3)(x^2-4x+2)b, x^4-6x^3+7x^2+2x-3=x^4-x^3-x^2+5x^3+5x^2+5x+3x^2-3x-3 =x^2(x^2-x-1)-5x(x^2-x-1)+3(x^2-x-1) =(x^2-x-1)(x^2-4x-4)c, x^4+x^3-27x^2-8x+12=x^4+5x^3-3x^2-4x^2+20x^2+12x-4x^2-20x+12 =x^2(x^2+5x-3)-4x(x^2+5x-3)-4(x^2+5x-3) =(x^2+5x-3)(x^2-4x-4)d, x^3-6x^2+11x-6=x^2-3x^2-3x^2+9x+2x-6 =x^2(x-3)-3x(x-3)+2(x-3) =(x-3)(x^2-3x+2) =(x-3)x^2-x-2x+2)