[tex]f(x) =x^5 -8x^3 +6x^2+7x-6\\\\= x^5 -2x^4+2x^4 -4x^3-4x^3+8x^2-2x^2+4x+3x -6\\\\=x^4(x-2) + 2x^3(x-2) -4x^2(x-2) -2x(x-2) +3(x-2)\\\\=(x-2)(x^4+2x^3-4x^2-2x+3)\\\\=(x-2)(x^4-x^3+3x^3-3x^2-x^2+x-3x+3)\\\\=(x-2)[x^3(x-1) +3x^2(x-1) -x(x-1) -3(x-1)]\\\\=(x-2)(x-1)(x^3 +3x^2 -x -3)\\\\=(x-2)(x-1)(x^3 -x^2 +4x^2-4x+3x-3)\\\\=(x-2)(x-1) [x^2(x-1)+4x(x-1) +3(x-1)]\\\\=(x-2)(x-1)(x-1) (x^2 +4x +3)\\\\=(x-2)(x-1)^2(x^2 +3x+x +3)\\\\=(x-2)(x-1)^2 [x(x+3) +(x+3)]\\\\=(x-2)(x-1)^2(x+1)(x+3)[/tex]
