Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]\text{We can notice that}\\\\(-3)^3+3(-3)^3+2(-3)+6=-27+27-6+6=0\\\\\text{So, we can factorise with }(x+3)\\\\x^3+3x^2+2x+6=\boxed{(x+3)(x^2+2)}[/tex]
If we are in [tex]\mathbb{C}[/tex], we can go further.
[tex]x^3+3x^2+2x+6=(x+3)(x^2+2)=(x+3)(x^2-(\sqrt{2}i)^2)\\\\=\boxed{(x+3)(x-\sqrt{2}i)(x+\sqrt{2}i)}[/tex]
Thanks
