Giải thích các bước giải:
a.Ta có:
$x^4+x^3+2x^2+x+1$
$=(x^4+2x^2+1)+(x^3+x)$
$=(x^2+1)^2+x(x^2+1)$
$=(x^2+1)(x^2+1+x)$
c.Ta có:
$x^4+6x^3+13x^2+12x+4$
$=(x^4+2x^3+x^2)+(4x^3+8x^2+4x)+(4x^2+8x+4)$
$=x^2(x^2+2x+1)+4x(x^2+2x+1)+4(x^2+2x+1)$
$=(x^2+2x+1)(x^2+4x+4)$
$=(x+1)^2(x+2)^2$
e.Ta có:
$x^4+10x^3+26x^2+10x+1$
$= (x^4+2x^2+1)+10(x^3+x)+24x^2$
$= (x^2+1)^2+10x(x^2+1)+24x^2$
$= (x^2+1)^2+2(x^2+1)\cdot 5x+(5x)^2-x^2$
$=(x^2+1+5x)^2-x^2$
$=(x^2+1+5x-x)(x^2+1+5x+x)$
$=(x^2+4x+1)(x^2+6x+1)$
g.Ta có:
$x^4+x^3-4x^2+x+1$
$=(x^4+2x^2+1) +(x^3+x)-6x^2$
$=(x^2+1)^2+x(x^2+1)-6x^2$
$=(x^2+1)^2+3x(x^2+1)-2x(x^2+1)-6x^2$
$=(x^2+1+3x)(x^2+1-2x)$
$=(x^2+3x+1)(x-1)^2$
