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How do you factor $x^{4} - 2 x^{3} + 5 x - 10$ $x^4-2x^3+5x-10$ ?

1 Answer

Feb 9, 2015

You can use a technique called factoring by grouping to factor this expression:

$x^{4} - 2 x^{3} + 5 x - 10$ $x^4-2x^3+5x-10$ Given
$(x^{4} - 2 x^{3}) + (5 x - 10)$ $(x^4-2x^3) + (5x-10)$ **Insert parenthesis **

This allows you to pair the terms with like factors and factor them.

$x^{3} (x - 2) + 5 (x - 2)$ $x^3(x-2) +5(x-2)$ Greatest Common Factor
$(x - 2) (x^{3} + 5)$ $(x-2)(x^3+5)$ **Undo Distributive Property **

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