\(x^5+x+1\)
\(=x^5-x^2+x^2+x+1\)
\(=x^2\left(x^3-1\right)+x^2+x+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^3-x^2\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
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Ta có :
x5 + x + 1
= x5 + x4 - x4 + x3 - x3 + x2 - x2 + x + 1
= x5 + x4 + x3 - x4 - x3 - x2 + x2 + x + 1
= x3( x2 + x + 1 ) - x2( x2 + x + 1) + ( x2 +x +1 )
= ( x2 + x + 1 )(x3 - x2 + 1)
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