Đáp án:
`x^7+x^5-1=(x^2-x+1)(x^5+x^4+x^3-x-1)`
`x^8-x+1=(x^2-x+1)(x^6+x^5-x^3-x^2+1)`
Giải thích các bước giải:
1,
`x^7+x^5+1`
`=x^7-x^6+x^5+x^6-x^5+x^4+x^5-x^4+x^3-x^3+x^2-x-x^2+x-1`
`=(x^7-x^6+x^5)+(x^6-x^5+x^4)+(x^5-x^4+x^3)-(x^3-x^2+x)-(x^2-x+1)`
`=x^5(x^2-x+1)+x^4(x^2-x+1)+x^3(x^2-x+1)-x(x^2-x+1)-(x^2-x+1)`
`=(x^2-x+1)(x^5+x^4+x^3-x-1)`
2,
`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^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(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^6+x^5-x^3-x^2+1)`
