Fatorar: $\phantom{X}x^3\,+\,1\phantom{X}$
resposta:
$\,x^3\,+\,1\,=\,x^3\,+\,1^3\,=$ $\,(x\,+\,1)(x^2\,-\,a\centerdot 1\,+\,1^2)\,=$ $\,(x\,+\,1)(x^2\,-\,x\,+1)\,$
×Fatorar: $\phantom{X}x^3\,+\,2x^2\,+\,2x\,+1\phantom{X}$
resposta:
Resolução:
$\,x^3\,+\,2x^2\,+\,2x\,+1\,=$ $\,x^3\,+\,1\,+\,2x^2\,+\,2x\,=$ $\,(x^3\,+\,1)\,+\,2x(x\,+\,1)\,=$ $\,(x\,+\,1)(x^2\,-\,x\,+\,1)\,+\,2x(x\,+\,1)\,=$ $\,(x\,+\,1)\left[\,(x^2\,-\,x\,+\,1)\,+\,2x\,\right]\,=$ $\,(x\,+\,1)(x^2\,+\,x\,+\,1)$
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