l: \(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
m: \(x^3+y^3-2\left(x^2-y^2\right)\)
\(=\left(x^3+y^3\right)-2\left(x^2-y^2\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-2\left(x-y\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-2x+2y\right)\)
p: \(\left(x^2+x+1\right)\left(x^2+x+2\right)-6\)
\(=\left(x^2+x\right)^2+2\left(x^2+x\right)+\left(x^2+x\right)+2-6\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-4\)
\(=\left(x^2+x\right)^2+4\left(x^2+x\right)-\left(x^2+x\right)-4\)
\(=\left(x^2+x\right)\left(x^2+x+4\right)-\left(x^2+x+4\right)\)
\(=\left(x^2+x+4\right)\left(x^2+x-1\right)\)
