Question

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

Answer 1

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

Explanation:

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.