Using the factor theorem it is found that \( a+b, b+c \) and \( c+a \) are three factors of the ...

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Using the factor theorem it is found that \( a+b, b+c \) and \( c+a \) are three factors of the determinant
\[
\left|\begin{array}{ccc}
-2 a & a+b & a+c \\
b+a & -2 b & b+c \\
c+a & c+b & -2 c
\end{array}\right|
\]
The other factor in the value of the determinant is
(A) 4
(B) \( a+b+c \)
(C) o
(D) none of these
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