algebra

Factor by grouping: 9x^4+9x^3+27x+27

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adoption $x_1=-1$

  ($x^4$ +  $x^3$+3x+3) : (x+1) = $x^3+3$

  $\underline{x^4+x^3}$

             0 $3x+3$

                $\underline{3x+3}$

                          0

$x^3+3=0\\ x_{2,3,4}=\sqrt[3]{-3} =-1.4422$

Factor by grouping: $9x^4+9x^3+27x+27$ = $9\times (x+1)\times (x-\sqrt[3]{-3})^3$

  !

$\displaystyle 9x^{4}+9x^{3}+27x+27 \\ = (9x^{4}+27x)+(9x^{3}+27) \\ =9x(x^{3}+3)+9(x^{3}+3) \\ = 9(x^{3}+3)(x+1).$