How do you factor completely $3 x^{2} - 21$ $3x^2 − 21$ ?

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Answer 1 · 2016-10-04T07:52:17

rational factors $3 (x^{2} - 7)$ $3(x^2-7)$
irrational facors $3 (x + \sqrt{7}) (x - \sqrt{7})$ $3(x+sqrt7)(x-sqrt7)$

Always look for a common factor first.

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

$3 (x^{2} - 7) \leftarrow$ $3(x^2 -7)" "larr$ there are no other rational factors

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

$3 (x + \sqrt{7}) (x - \sqrt{7})$ $3(x+sqrt7)(x-sqrt7)$

How do you factor completely 3x^2 − 213x2−213x^2 − 21?