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

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

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Answer 1 · 2015-05-01T19:26:35

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

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

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

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

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

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

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