Question

Factor completely 3x2 - 21.

Answer 1

3x² - 21

Factor 3 from both terms:

3 (x² - 7)

To me, that's as far as you should need to go.  But if you want to get
completely carried away, you could go one step further, since you have
the difference of two squares:

3 (x + √7) (x - √7)

Of course, there's no end now, because the last binomial could be
considered another difference of two squares, so you'd have to
factor that too:

3 (x + √7) (√x + ⁴√7) (√x - ⁴√7)

but to me, this would be nonsense.

Answer 2

$3x^2-21=3(x^2-7)=3[x^2-(\sqrt7)^2]=3(x-\sqrt7)(x+\sqrt7)$