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

  !

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