`1) x^11+x^4+1`
`=x^11+ x^10 + x^9 - x^10 - x^9 - x^8 +x^8 + x^7 + x^6 - x^7 - x^6 - x^5 + x^5 + x^4 + x^3 - x^3 + 1.`
`=(x^11+ x^10 + x^9) - (x^10 + x^9 + x^8) +(x^8 + x^7 + x^6) - (x^7 + x^6 + x^5) + (x^5 + x^4 + x^3) - (x^3 - 1).`
`= x^9(x^2+x+1) -x^8(x^2+x+1) +x^6(x^2+x+1) -x^5(x^2+x+1) + x^3(x^2+x+1) - (x-1)(x^2+x+1).`
`=(x^2+x+1)(x^9-x^8+x^6-x^5+x^3 - x +1 ).`
`2) x^11 + x^7 + 1`
`= x^11 + x^10 + x^9 - x^10 - x^9 - x^8 + x^8 + x^7 + x^6 - x^6 - x^5 - x^4 + x^5 + x^4 + x^3 - x^3 + 1`
`= (x^11 + x^10 + x^9) - ( x^10 + x^9 + x^8) + (x^8 + x^7 + x^6) - ( x^6 + x^5+ x^4) +( x^5 + x^4 + x^3) - (x^3 - 1)`
`= x^9(x^2+x+1) -x^8(x^2+x+1) + x^6(x^2+x+1) - x^4(x^2+x+1) + x^3(x^2+x+1) - (x-1)(x^2+x+1).`
`= (x^2+x+1)(x^9-x^8+x^6-x^4+x^3-x+1).`
