Which of the following is a factor of the determinant $\begin{vmatrix} a & b & c\\b & c & a\\c & a & b\end{vmatrix}$ ?

$a+b+c$

The correct answer is Option (2) → $a+b+c$

$Δ=\begin{vmatrix} a & b & c\\b & c & a\\c & a & b\end{vmatrix}$

$C_1→C_1+C_2+C_3$

$\begin{vmatrix} a+b+c & b & c\\a+b+c & c & a\\a+b+c & a & b\end{vmatrix}$

$=(a+b+c)\begin{vmatrix} 1 & b & c\\1 & c & a\\1 & a & b\end{vmatrix}$

$⇒(a+b+c)$ is a better