Question

Factorise:
x³ − 3x² + x − 3

Answer 1

We have:
$$\begin{gathered} x^3-3x^2+x-3=\left(x^3-3x^2\right)+\left(x-3\right) \\ =x^2\left(x-3\right)+1\left(x-3\right) \\ =\left(x-3\right)\left(x^2+1\right) \end{gathered}$$

∴ $x^3-3x^2+x-3=\left(x-3\right)\left(x^2+1\right)$