How do you factor $x^3+3x^2-2x-6$ ?

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Answer 1 · 2016-09-09T18:32:55

$(x + 3)(x + sqrt(2))(x - sqrt(2))$

We have: $x^(3) + 3 x^(2) - 2 x - 6$

$= (x^(3) + 3 x^(2)) + (- 2 x - 6)$

Let's take $x^(2)$ in common in the first set of parentheses and $- 2$ in common in the second set of parentheses, respectively:

$= (x^(2) (x + 3)) + (- 2 (x + 3))$

$= x^(2) (x + 3) - 2 (x + 3)$

Then, let's take $x + 3$ in common:

$= (x + 3) (x^(2) - 2)$

If you allow surds to be used, then the second set of parentheses can be factorised further:

$= (x + 3)(x + sqrt(2))(x - sqrt(2))$

How do you factor x^3+3x^2-2x-6x^3+3x^2-2x-6?