Đáp án:
`e)(x^2+x+1)(x^3-x+1)`
`f)(x^2+x+1)(x^6-x^5+x^3-x^2+1)`
Giải thích các bước giải:
`e)x^5+x^4+1`
`=x^5+x^4+x^2-x^2+1`
`=(x^5-x^2)+(x^4+x^2+1)`
`=x^2(x^3-1)+(x^4+2x^2-x^2+1)`
`=x^2(x-1)(x^2+x+1)+[(x^4+2x^2+1)-x^2]`
`=(x^3-x^2)(x^2+x+1)+{[(x^2)^2+2.x^2 .1+1^2]-x^2}`
`=(x^3-x^2)(x^2+x+1)+[(x^2+1)^2-x^2]`
`=(x^3-x^2)(x^2+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)`
`f)x^8+x+1`
`=x^8+x^2-x^2+x+1`
`=(x^8-x^2)+(x^2+x+1)`
`=x^2(x^6-1)+(x^2+x+1)`
`=x^2[(x^3)^2-1^2]+(x^2+x+1)`
`=x^2(x^3+1)(x^3-1)+(x^2+x+1)`
`=(x^5+x^2)(x-1)(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1)[(x^5+x^2)(x-1)+1]`
`=(x^2+x+1)(x^6-x^5+x^3-x^2+1)`
