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

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

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Answer 1 · 2016-11-24T00:39:17

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

Explanation:

Separate out a common factor $- x$ $-x$ and rearrange in descending order of powers of $x$ $x$ . Then find a pair of numbers with product $6$ $6$ and difference $1$ $1$ . The pair $3$ $3$ , $2$ $2$ works, so we find:

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

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

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