Question

How do you factor completely `3x^2 − 21`?

Answer 1

rational factors `3(x^2-7)`
irrational facors `3(x+sqrt7)(x-sqrt7)`

Explanation:

Always look for a common factor first.

`3x^2 -21" "larr` there is a common factor of 3

`3(x^2 -7)" "larr` there are no other rational factors

However, as this is in the form of the difference of squares, we could show irrational factors as:

`3(x+sqrt7)(x-sqrt7)`