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

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Answer 1 · 2016-12-16T01:11:25

$3x^3+9x^2+x+3 = (3x^2+1)(x + 3)$

This factors by grouping, as:
$3x^3+9x^2+x+3 = 3x^2*x + 3x^2*3+x+3$
$" " = 3x^2(x + 3)+(x+3)$
$" " = (3x^2+1)(x + 3)$

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

How do you factor completely 3x^3+9x^2+x+33x^3+9x^2+x+3?