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

Oct 4, 2016

#### Answer:

rational factors $3 \left({x}^{2} - 7\right)$
irrational facors $3 \left(x + \sqrt{7}\right) \left(x - \sqrt{7}\right)$

#### Explanation:

Always look for a common factor first.

$3 {x}^{2} - 21 \text{ } \leftarrow$ there is a common factor of 3

$3 \left({x}^{2} - 7\right) \text{ } \leftarrow$ there are no other rational factors

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

$3 \left(x + \sqrt{7}\right) \left(x - \sqrt{7}\right)$