Đáp án:
$a)(x-1)(x-2)\left(x^2-x+1\right)\\ b)(2x+1)(2x-3)\left(x^2+3x+3\right)\\ c)(x^2-x+2)(x^2+x+1)\\ d)(x^2-x+2)(3x^2+x+1)$
Giải thích các bước giải:
$a)x^4-4x^3+6x^2-5x+2\\ =x^4-4x^3+6x^2-5x+2\\ =x^4-x^3-3x^3+3x^2+3x^2-3x-2x+2\\ =x^3(x-1)-3x^2(x-1)+3x(x-1)-2(x-1)\\ =(x-1)(x^3-3x^2+3x-2)\\ =(x-1)(x^3-2x^2-x^2+2x+x-2)\\ =(x-1)\left(x^2(x-2)-x(x-2)+x-2\right)\\ =(x-1)(x-2)\left(x^2-x+1\right)\\ b)4x^4+8x^3-3x^2-21x-9\\ =4x^4+2x^3+6x^3+3x^2-6x^2-3x-18x-9\\ =2x^3(2x+1)+3x^2(2x+1)-3x(2x+1)-9(2x+1)\\ =(2x+1)\left(2x^3+3x^2-3x-9\right)\\ =(2x+1)\left(2x^3-3x^2+6x^2-9x+6x-9\right)\\ =(2x+1)\left(x^2(2x-3)+3x(2x-3)+3(2x-3)\right)\\ =(2x+1)(2x-3)\left(x^2+3x+3\right)\\ c)x^4+2x^2+x+2\\ =x^4+2x^2+1-x^2+x^2+x+1\\ =(x^2+1)^2-x^2+x^2+x+1\\ =(x^2+1-x)(x^2+1+x)+x^2+x+1\\ =(x^2+1-x)(x^2+x+1)+x^2+x+1\\ =(x^2+1-x+1)(x^2+x+1)\\ =(x^2-x+2)(x^2+x+1)\\ d)3x^4-2x^3+6x^2+x+2\\ =x^4+2x^2+x+2+2x^4-2x^3+4x^2\\ =x^4+2x^2+1-x^2+x^2+x+1+2x^2(x^2-x+2)\\ =(x^2+1)^2-x^2+x^2+x+1+2x^2(x^2-x+2)\\ =(x^2+1-x)(x^2+1+x)+x^2+x+1+2x^2(x^2-x+2)\\ =(x^2+1-x)(x^2+x+1)+x^2+x+1+2x^2(x^2-x+2)\\ =(x^2+1-x+1)(x^2+x+1)+2x^2(x^2-x+2)\\ =(x^2-x+2)(x^2+x+1)+2x^2(x^2-x+2)\\ =(x^2-x+2)(x^2+x+1+2x^2)\\ =(x^2-x+2)(3x^2+x+1)$
