Đáp án: + Giải thích các bước giải:
Bài $5$.
$2x^5 - 3x^4 +6x^3 -8x^2 +3$
$= 2x^5 - 2x^4 - x^4 + x^3 + 5x^3 - 5x^2 - 3x^2 + 3x - 3x + 3$
$= 2x^4(x-1) -x^3(x-1) + 5x^2(x-1) - 3x(x-1) - 3(x-1)$
$= (x-1)(2x^4 - x^3 + 5x^2 - 3x - 3)$
$= (x-1)(2x^4 - 2x^3 + x^3 -x^2 + 6x^2 - 6x + 3x-3)$
$= (x-1)[2x^3(x-1) + x^2(x-1) + 6x(x-1) + 3(x-1)]$
$= (x-1)^2 .(2x^3 + x^2 + 6x + 3)$
$= (x-1)^2 .[x^2(2x+1) + 3(2x+1)]$
$= (x-1) . (2x+1)(x^2+3)$.
Bài $6$. $x^5 - 5x^4 + 4x^3 +4x^2 - 5x +1$
$= x^5 - x^4 -4x^4 + 4x^3 + 4x^2 - 4x - x + 1$
$= x^4(x-1) - 4x^3(x-1) + 4x(x-1) - (x-1)$
$= (x-1)(x^4 - 4x^3 + 4x - 1)$
$= (x-1)(x^4 - x^3 - 3x^3 + 3x^2 - 3x^2 + 3x + x - 1)$
$= (x-1)[x^3(x-1) - 3x^2(x-1) - 3x(x-1) + (x-1)]$
$= (x-1)^2 .(x^3 - 3x^2 - 3x + 1)$
$= (x-1)^2 .(x^3 - 4x^2 + x + x^2 - 4x + 1)$
$= (x-1)^2 .[x(x^2-4x+1) + (x^2-4x+1)]$
$= (x-1)^2 . (x+1)(x^2-4x+1)$.