`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).`

$x^{11} + x^{4} + 1$

$= (x^{11} + x^{10} + x^{9}) - (x^{10} + x^{9} + x^{8}) + (x^{8} + x^{7} + x^{6}) - (x^{7} + x^{6} + x^{5}) + (x^{5} + x^{4} + x^{3}) - (x^{3} + x^{2} + x) + (x^{2} + x + 1)$

$= x^{9}(x^{2} + x + 1) - x^{8}(x^{2} + x + 1) + x^{6}(x^{2} + x + 1) - x^{5}(x^{2} + x + 1) + x^{3}(x^{2} + x + 1) - x^{2}(x^{2} + x + 1) + (x^{2} + x + 1)$

$= (x^{2} + x + 1)(x^{9} - x^{8} + x^{6} - x^{5} + x^{3} - x^{2} + 1)$

$x^{11} + x^{7} + 1$

$= (x^{11} + x^{10} + x^{9}) - (x^{10} + x^{9} + x^{8}) + (x^{8} + x^{7} + x^{6}) - (x^{6} + x^{5} + x^{4}) + (x^{5} + x^{4} + x^{3}) - (x^{4} + x^{3} + x^{2}) + (x^{2} + x + 1)$

$= x^{9}(x^{2} + x + 1) - x^{8}(x^{2} + x + 1) + x^{6}(x^{2} + x + 1) - x^{4}(x^{2} + x + 1) + x^{3}(x^{2} + x + 1) - x^{2}(x^{2} + x + 1) + (x^{2} + x + 1)$

$= (x^{2} + x + 1)(x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x^{2} + 1)$