Factorize: ${\mathrm{x}}^3-6{\mathrm{x}}^2+3\mathrm{x}-18$

The given expression: ${\mathrm{x}}^3 - 6{\mathrm{x}}^2 + 3\mathrm{x} - 18$

By Grouping, we get:

${\mathrm{x}}^{3 }- 6{\mathrm{x}}^2 + 3\mathrm{x} - 18 = ({\mathrm{x}}^3 - 6{\mathrm{x}}^2) + (3\mathrm{x} - 18)$

Now, by taking out the common factors,

${\mathrm{x}}^3 - 6{\mathrm{x}}^2 + 3\mathrm{x} - 18 = {\mathrm{x}}^2(\mathrm{x} - 6) + 3(\mathrm{x} - 6)$

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

Therefore, the factors are $({\mathrm{x}}^2 + 3)(\mathrm{x} - 6)$.