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

Đáp án: g)x^5+x^4+1=x^5-x^2+x^4-x+x^2+x+1=x^2(x-1)(x^2+x+1)+x(x-1)(x^2+x+1)+x^2+x+1=(x^2+x+1)(x^3-x^2+x^2-x+1)=(x^2+x+1)(x^3-x+1)

h) x^5+x+1=x^5-x^2+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)

i)x^8+x^7+1=x^8-x^2+x^7-x+x^2+x+1=x^2(x^6-1)+x(x^6-1)+x^2+x+1=x^2(x^3+1)(x-1)(x^2+x+1)+x(x^3+1)(x-1)(x^2+x+1)+(x^2+x+1)=(x^2+x+1)(x^6+x^3-x^4-x+1)

k) x^5-x^4-1=x^5+x^2-x^4-x-x^2+x-1=x^2(x+1)(x^2-x+1)-x(x+1)(x^2-x+1)-(x^2-x+1)=(x^2-x+1)(x^3+x^2-x^2-x-1)=(x^2-x+1)(x^3-x-1)

l)x^7+x^5+1=x^7-x+x^5-x^2+x^2+x+1=x(x^3+1)(x^3-1)+x^2(x^3-1)+(x^2+x+1)=x(x^3+1)(x-1)(x^2+x+1)+x^2(x-1)(x^2+x+1)+(x^2+x+1)=(x^2+x+1)(x^5-x^4+x^3-x+1)

m)x^8+x^4+1=x^8-x^2+x^4-x+x^2+x+1=x^2(x^3+1)(x^3-1)+x(x^3-1)+x^2+x+1=x^2(x^3+1)(x-1)(x^2+x+1)+x(x-1)(x^2+x+1)+(x^2+x+1)=(x^2+x+1)(x^6-x^5+x^3-x+1)