Giải thích các bước giải:
a/ $4x^3-14x^2+6x$
$=2x(2x^2-7x+3)$
$=2x(2x^2-6x-x+3)$
$=2x(x-3)(2x-1)$
b/ $x^3+4x^2-29x+24$
$=x^3+8x^2-4x^2-32x+3x+24$
$=(x+8)(x^2-4x+3)$
$=(x+8)(x^2-3x-x+3)$
$=(x+8)(x-3)(x-1)$
c/ $x^3+21x^2+134x+240$
$=x^3+10x^2+11x^2+110x+24x+240$
$=(x+10)(x^2+11x+24)$
$=(x+10)(x^2+3x+8x+24)$
$=(x+10)(x+3)(x+8)$
d/ $x^4+64$
$=x^4+16x^2+64-16x^2$
$=(x^2+8)^2-16x^2$
$=(x^2+8-4x)(x^2+8+4x)$
$=(x^2-4x+8)(x^2+4x+8)$
e/ $x^4+4y^4$
$=x^4+4x^2y^2+4y^4-4x^2y^2$
$=(x^2+2y^2)^2-4x^2y^2$
$=(x^2+2y^2-2xy)(x^2+2y^2+2xy)$
$=(x^2-2xy+2y^2)(x^2+2xy+y^2)$
f/ $x^5+x^4+1$
$=x^5-x^2+x^4-x+x^2+x+1$
$=x^2(x^3-1)+x(x^3-1)+x^2+x+1$
$=x^2(x-1)(x^2+x+1)+x(x-1)(x^2+x+1)+(x^2+x+1)$
$=(x^2+x+1)(x^3-x^2+x^2-x+1)$
$=(x^2+x+1)(x^3-x+1)$
g/ $x^8+x^4+1$
$=x^8-x^2+x^4-x+x^2+x+1$
$=x^2(x^6-1)+x(x^3-1)+(x^2+x+1)$
$=x^2(x^3+1)(x-1)(x^2+x+1)+x(x-1)(x^2+x+1)+(x^2+x+1)$
$=(x^2+x+1)[x^2(x^3+1)(x-1)+x(x-1)+1]$
$=(x^2+x+1)[(x^5+x^2)(x-1)+x^2-x+1]$
$=(x^2+x+1)(x^6-x^5+x^3-x^2+x^2-x+1)$
$=(x^2+x+1)(x^6-x^5+x^3-x+1)$
h/ $x^7+x^2+1$
$=x^7-x+x^2+x+1$
$=x(x^6-1)+(x^2+x+1)$
$=x(x^3+1)(x-1)(x^2+x+1)+(x^2+x+1)$
$=(x^2+x+1)[x(x^3+1)(x-1)+1]$
$=(x^2+x+1)[(x^4+x)(x-1)+1]$
$=(x^2+x+1)(x^5-x^4+x^2-x+1)$
i/ $x^{10}+x^5+1$
$=x^{10}-x+x^5-x^2+x^2+x+1$
$=x(x^9-1)+x^2(x^3-1)+(x^2+x+1)$
$=x(x^3-1)(x^6+x^3+1)+x^2(x-1)(x^2+x+1)+(x^2+x+1)$
$=x(x^6+x^3+1)(x-1)(x^2+x+1)+x^2(x-1)(x^2+x+1)+(x^2+x+1)$
$=(x^2+x+1).[x(x^6+x^3+1)(x-1)+x^2(x-1)+1]$
$=(x^2+x+1)[(x^7+x^4+x)(x-1)+x^3-x^2+1]$
$=(x^2+x+1)(x^8-x^7+x^5-x^4+x^2-x+x^3-x^2+1)$
$=(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1)$
Chúc bạn học tốt !!!
