How do you factor $x^{3} - 2 x^{2} - 5 x + 10$ $x^3 - 2x^2 - 5x + 10$ ?

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How do you factor $x^{3} - 2 x^{2} - 5 x + 10$ $x^3 - 2x^2 - 5x + 10$ ?

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Answer 1 · 2015-12-20T07:22:30

Apply factoring by grouping to obtain

$x^{3} - 2 x^{2} - 5 x + 10 = (x^{2} - 5) (x - 2)$ $x^3-2x^2-5x+10 = (x^2-5)(x-2)$

Explanation:

By grouping:

$x^{3} - 2 x^{2} - 5 x + 10 = x^{2} (x - 2) - 5 (x - 2)$ $x^3-2x^2-5x+10 = x^2(x-2)-5(x-2)$

$= (x^{2} - 5) (x - 2)$ $= (x^2-5)(x-2)$

We could further factor $x^{2} - 5 = (x + \sqrt{5}) (x - \sqrt{5})$ $x^2-5 = (x+sqrt(5))(x-sqrt(5))$ by the difference of squares technique, however the above suffices if we only want a solution involving integers.

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How do you factor $x^{3} - 2 x^{2} - 5 x + 10$ $x^3 - 2x^2 - 5x + 10$ ?

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How do you factor x^3 - 2x^2 - 5x + 10x3−2x2−5x+10x^3 - 2x^2 - 5x + 10?

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How do you factor $x^{3} - 2 x^{2} - 5 x + 10$ $x^3 - 2x^2 - 5x + 10$ ?