How do I factorise a cubic polynomial like x³ − 6x² + 11x − 6?

For a cubic, first find one factor using the factor theorem, then reduce it to a quadratic. Try small integer values that divide the constant term 6, such as 1, 2, 3. Substitute x = 1: 1 − 6 + 11 − 6 = 0, so (x − 1) is a factor. Now divide x³ − 6x² + 11x − 6 by (x − 1) using long division or synthetic division, giving x² − 5x + 6. Factorise this quadratic into (x − 2)(x − 3). So the full factorisation is (x − 1)(x − 2)(x − 3). The strategy is always the same: find one root by trial using factors of the constant, then break the leftover quadratic the usual way.