Lời giải:
a. $x^4+4=(x^2)^2+2^2+2.x^2.2-4x^2$
$=(x^2+2)^2-(2x)^2=(x^2+2-2x)(x^2+2+2x)$
b. $x^4+324=(x^2)^2+18^2+2.x^2.18-36x^2$
$=(x^2+18)^2-(6x)^2=(x^2+18-6x)(x^2+18+6x)$
c. $x^7+x^5+1=(x^7-x)+(x^5-x^2)+x^2+x+1$
$=x(x^6-1)+x^2(x^3-1)+(x^2+x+1)$
$=x(x^3-1)(x^3+1)+x^2(x^3-1)+(x^2+x+1)$
$=(x^3-1)(x^4+x+x^2)+(x^2+x+1)$
$=(x-1)(x^2+x+1)(x^4+x^2+x)+(x^2+x+1)$
$=(x^2+x+1)[(x-1)(x^4+x^2+x)+1]$
$=(x^2+x+1)(x^5-x^4+x^3-x+1)$
d. $x^5+x-1=x^5+x^2-(x^2-x+1)$
$=x^2(x^3+1)-(x^2-x+1)=x^2(x+1)(x^2-x+1)-(x^2-x+1)$
$=(x^2-x+1)(x^3+x^2-1)$
a) \(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b) \(x^4+324\)
\(=x^4+36x^2+324-36x^2\)
\(=\left(x^2+18\right)^2-\left(6x\right)^2\)
\(=\left(x^2-6x+18\right)\left(x^2+6x+18\right)\)
