Đáp án:
Giải thích các bước giải:
`a,`
`x^{10} + x^5 + 1 `
`=x^{10} -x + x^5 - x^2 + x^2 + x +1`
`= x(x^9 -1) + x^2(x^3-1) + (x^2 + x+1)`
`=x(x^3-1)(x^3+1) + x^2 (x^3-1) + (x^2 + x+1)`
`=x(x-1)(x^2+x+1)(x^3+1) + x^2(x-1)(x^2+x+1) + (x^2+x+1)`
`=(x^2 + x + 1)[(x(x-1)(x^3+1) + x^2(x-1)]`
`=(x^2 + x+1)[x^5+x^2-x^4-x+x^3-x^2+1]`
`=(x^2 +x+1)(x^5-x^4+x^3+1)`
`b,`
`x^5 - x^4 -1`
`=x^5 + x^2 - x^4 -x -x^2 + x-1`
`=x^2(x^3+1) - x(x^3+1) - (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^2(x+1) - x(x+1) - 1]`
`=(x^2-x+1)[x^3+x^2-x^2-x-1]`
`=(x^2-x+1)(x^3-x-1)`
Chúc bạn học tốt~
