# How do you factor completely 3x^3+9x^2+x+3?

Dec 16, 2016

$3 {x}^{3} + 9 {x}^{2} + x + 3 = \left(3 {x}^{2} + 1\right) \left(x + 3\right)$

#### Explanation:

This factors by grouping, as:
$3 {x}^{3} + 9 {x}^{2} + x + 3 = 3 {x}^{2} \cdot x + 3 {x}^{2} \cdot 3 + x + 3$
$\text{ } = 3 {x}^{2} \left(x + 3\right) + \left(x + 3\right)$
$\text{ } = \left(3 {x}^{2} + 1\right) \left(x + 3\right)$

The quadratic term does not factorise further, so this is the fully factorised form.