Factor completely:

\[ 3x^2 - 21 \]

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.

Answered by AL2006 | 2024-06-10

3 x 2 − 21 = 3 ( x 2 − 7 ) = 3 [ x 2 − ( 7 ​ ) 2 ] = 3 ( x − 7 ​ ) ( x + 7 ​ )

Answered by Anonymous | 2024-06-10

The expression 3 x 2 − 21 can be factored by first pulling out the common factor of 3, giving 3 ( x 2 − 7 ) . This further factors to 3 ( x − 7 ​ ) ( x + 7 ​ ) , resulting in the complete factorization. Thus, the final answer is 3 ( x − 7 ​ ) ( x + 7 ​ ) .
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Answered by AL2006 | 2024-09-26