Question

X^3+ 3x^2 + 2x + 6 factor

Answer 1

Answer:

Step-by-step explanation:

Hello, please consider the following.

$\text{We can notice that}\\\\(-3)^3+3(-3)^3+2(-3)+6=-27+27-6+6=0\\\\\text{So, we can factorise with }(x+3)\\\\x^3+3x^2+2x+6=\boxed{(x+3)(x^2+2)}$

If we are in $\mathbb{C}$, we can go further.

$x^3+3x^2+2x+6=(x+3)(x^2+2)=(x+3)(x^2-(\sqrt{2}i)^2)\\\\=\boxed{(x+3)(x-\sqrt{2}i)(x+\sqrt{2}i)}$

Thanks