# Is it possible to factor y=x^3 - 2x^2 + 3x -6 ? If so, what are the factors?

May 28, 2016

$\left(x - 2\right) \left({x}^{2} + 3\right)$

#### Explanation:

Group the terms in 'pairs' thus

$\left[{x}^{3} - 2 {x}^{2}\right] + \left[3 x - 6\right]$

now factorise each 'pair'

${x}^{2} \left(x - 2\right) + 3 \left(x - 2\right)$

A common factor of (x -2) can now be removed

$\Rightarrow \left(x - 2\right) \left({x}^{2} + 3\right)$