Factorising determinantsAQA A-Level Further Maths: Mind map

Exam questions on Factorising determinants

1. Let $\Delta=\begin{vmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{vmatrix}$.
   Use a column operation to show that $(x+2)$ is a factor of $\Delta$.2 marks
2. Let $\Delta=\begin{vmatrix} 1 & 1 & 1 \\ x & 2 & 3 \\ x^2 & 4 & 9 \end{vmatrix}$.
   Explain why $(x-2)$ is a factor of $\Delta$.2 marks
3. Let $\Delta=\begin{vmatrix} x+1 & 2 & 3 \\ 1 & x+2 & 3 \\ 1 & 2 & x+3 \end{vmatrix}$.
   Show that $(x+6)$ is a factor of $\Delta$.3 marks