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

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Answer 1 · 2015-05-01T19:26:35

$x^3-x^2-6x+6$

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

$=(x^2)(x-1)-(6)(x-1)$

$=(x^2-6)(x-1)$

...if you wanted you could continue to factor:
$=(x-sqrt(6))(x+sqrt(6))(x-1)$
but is this really any improvement?

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