# Determinant Factorisation

Lunat1c
Is there a good method or any particular way you guys use to factorise determinant to avoid staring at a problem for minutes without coming up with any answers?

Lets say I want to factorize $$\begin{bmatrix} 1 & a & a+1 \\ a+1 & 1 & a \\ a & a+1 & 1 \end{bmatrix}$$

Where should I start? Is there a general way to do this so that the process is a bit quick especially for when it comes to exams? Thanks!

Staff Emeritus