Giải thích các bước giải:
x^ 5-5x^3+ 2x^2+ 6x -4
=x^5-x^4+x^4-x^3-4x^3+4x^2-2x^2+2x+4x-4
=(x^5-x^4)+(x^4-x^3)-(4x^3-4x^2)-(2x^2-2x)+(4x-4)
=x^4(x-1)+x^3(x-1)-4x^2(x-1)-2x(x-1)+4(x-1)
=(x-1)(x^4+x^3-4x^2-2x+4)
=(x-1)(x^4-x^3+2x^3-2x^2-2x^2+2x-4x+4)
=(x-1)[x^3(x-1)+2x^2(x-1)-2x(x-1)-4(x-1)]
=(x-1)^2.(x^3+2x^2-2x-4)
=(x-1)^2.[x^2(x+2)-2(x+2)]
=(x-1)^2.(x+2).(x^2-2)