# How do you factor #x^3 -x^2 + x -6 = 0#?

##### 1 Answer

Derived by substitution and observation.

#### Explanation:

Given:

Factors of 6 are {1,6} ; {2,3}

So

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Try

Try

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So we have

Building by 1 term at a time.

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But

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To 'force'

So our next number is

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So our next number is 3 giving

We have now built all the terms

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The latter bracket can not be split into any further whole number factorisations so we stop.

The only whole number factors of 3 is {1,3} and