Question

Factorise x(x+2)(x²+6x+12)​

Answer 1

x (x+2) (x² + 6x + 12)

x ² + 2x + x³ + 6 x² + 12x

x³ + 7x²  + 14x

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Answer 2

$x(x+2)(x^2+6x+12) \\ \\ x(x+2)(x^2+(3+\iota\sqrt{3})x+(3-\iota\sqrt{3})x+12) \\ \\ x(x+2)(x(x+3+\iota\sqrt{3})+(3-\iota\sqrt{3})(x+3+\iota\sqrt{3})) \\ \\ x(x+2)(x+3+\iota\sqrt{3})(x+3-\iota\sqrt{3}) \\ \\ \\ \large \textit{Thus, factorized, and the roots are,} \\ \\ x=0,\ \ -2,\ \ -3-\iota\sqrt{3},\ \ \iota\sqrt{3}-3 \\ \\ \\ \textit{where \ \iota=\sqrt{-1} }$