If Delta = begin{vmatrix} a + x & b & c b & | vedclass

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(B) To find the factors of the determinant $\Delta = \begin{vmatrix} a + x & b & c \ b & x + c & a \ c & a & x + b \end{vmatrix}$,we apply the colum

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$x + (a + b + c)$

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(B) To find the factors of the determinant $\Delta = \begin{vmatrix} a + x & b & c \ b & x + c & a \ c & a & x + b \end{vmatrix}$,we apply the column operation $C_1 	o C_1 + C_2 + C_3$. Performing this operation,the first column becomes: $C_1 	o \begin{bmatrix} (a + x) + b + c \ b + (x + c) + a \ c + a + (x + b) \end{bmatrix} = \begin{bmatrix} x + a + b + c \ x + a + b + c \ x + a + b + c \end{bmatrix}$. Now,we can factor out $(x + a + b + c)$ from the first column: $\Delta = (x + a + b + c) \begin{vmatrix} 1 & b & c \ 1 & x + c & a \ 1 & a & x + b \end{vmatrix}$. Since $(x + a + b + c)$ is a common factor of the determinant,the correct option is $B$.

If $\Delta = \begin{vmatrix} a + x & b & c \\ b & x + c & a \\ c & a & x + b \end{vmatrix}$,which of the following is a factor for the above determinant?

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