~ gửi bạn ~
`1) x^7 + x^2 + 1`
`= x^7 + x^6 - x^6 + x^5 - x^5 + x^4 - x^4 +x^3 - x^3 +2x^2 - x^2 +x - x +1`
`=(x^7 + x^6 + x^5) - (x^6 +x^5 +x^4) + (x^4 + x^3 +x^2) - (x^3 +x^2 + x) + (x^2 + x +1)`
`=x^5(x^2 + x + 1) - x^4(x^2 + x + 1) +x^2(x^2 + x + 1) - x(x^2 + x + 1) + (x^2 + x + 1)`
`=(x^2 + x + 1)(x^5 - x^4 +x^2 -x +1)`
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`2) x^7 + x^5 + 1`
`= (x^7−x)+(x^5−x^2)+(x^2+x+1) `
`= x(x^6−1)+x^2(x^3−1)+(x^2+x+1)`
`= x[(x^3)^2−1]+x^2(x−1)(x^2+x+1)+(x^2+x+1)`
`= x(x^3−1)(x^3+1)+x^2(x−1)(x^2+x+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)+1]`
`= ( x^2 + x + 1 ) ( x^ 5 − x ^4 + x ^3 − x + 1 )`
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`3) x^5 + x^4 + 1`
`=(x^5+x^4+x^3)−(x^3−1)`
`= x^3(x^2+x+1)−(x−1)(x^2+x+1)`
`=(x^2+x+1)(x^3−x+1)`
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`4) x^5 + x + 1`
`= x^5+x^4+x^3-x^4-x^3-x^2+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^3 - x^2 + 1)`
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`5) x^8 + x^7 + 1`
`= x^8+x^7+x^6+x^5+x^4+x^3+x^2+x-x^6-x^5-x^4-x^3-x^2-x+1`
`= x^6(x^2+x+1)+x^3(x^2+x+1)+(x^2+x+1)-x^4(x^2+x+1)-x(x^2+x+1)`
`= (x^2+x+1)(x^6+x^3+1-x^4-x)`
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`6) x^6 - x^4 - 1`
(mik ko biết làm)
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`7) x^5 + x - 1`
`=(x^5+x^2)−(x^2−x+1)`
`= x^2(x^3+1)−(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)`
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`8) x^10 + x^5 + 1`
`=x^10-x+x^5-x^2+x^2+x+1`
`=x.(x^9-1)+x2.(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)+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-x+1)`
