g) x^5 +x^4 +1 h) x^5 +x +1 i) x^8 +x^7 +1 k) x^5 - x^4 -1 l) x^7 + x^5 +1 m) x^8 +x^4 +1 lam ra giay part2 nha

\[\begin{array}{l} g)\,\,\,{x^5} + {x^4} + 1 = {x^5} - {x^2} + {x^4} + {x^2} + 1\\ = {x^2}\left( {{x^3} - 1} \right) + \left( {{x^4} + {x^2} + 1} \right)\\ = {x^2}\left( {x - 1} \right)\left( {{x^2} + x + 1} \right) + \left( {{x^4} + 2{x^2} + 1 - {x^2}} \right)\\ = {x^2}\left( {x - 1} \right)\left( {{x^2} + x + 1} \right) + {\left( {{x^2} + 1} \right)^2} - {x^2}\\ = {x^2}\left( {x - 1} \right)\left( {{x^2} + x + 1} \right) + \left( {{x^2} - x + 1} \right)\left( {{x^2} + x + 1} \right)\\ = \left( {{x^2} + x + 1} \right)\left( {{x^3} - {x^2} + {x^2} - x + 1} \right)\\ = \left( {{x^2} + x + 1} \right)\left( {{x^3} - x + 1} \right).\\ h)\,\,{x^5} + x + 1 = {x^5} - {x^2} + {x^2} + x + 1\\ = {x^2}\left( {{x^3} - 1} \right) + {x^2} + x + 1\\ = {x^2}\left( {x - 1} \right)\left( {{x^2} + x + 1} \right) + {x^2} + x + 1\\ = \left( {{x^2} + x + 1} \right)\left( {{x^3} - {x^2} + 1} \right).\\ m)\,\,{x^8} + {x^4} + 1 = {\left( {{x^4}} \right)^2} + 2{x^4} + 1 - 2{x^4}\\ = {\left( {{x^4} + 1} \right)^2} - 2{x^4} = \left( {{x^4} + 1 - \sqrt 2 {x^2}} \right)\left( {{x^4} + 1 + \sqrt 2 {x^2}} \right). \end{array}\]