\(x^7+x^5+1\)
\(=x^7+x^6+x^5-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)
\(=x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^5-x^4+x^3-x+1\right)\left(x^2+x+1\right)\)
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Cách 2 .
x7 + x5 + 1
= x7 + x6 + x5 - x6 + 1
= x5( x2 + x + 1) - [ ( x3 )2 - 1]
= x5( x2 + x + 1) - ( x3 - 1)( x3 + 1)
= x5( x2 + x + 1) -( x - 1)( x2 + x + 1)( x3 + 1)
= ( x2 + x + 1)[ x5 -( x - 1)( x3 + 1)]
= (x2 + x + 1)( x5 - x4 + x3 - x + 1)
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