Using the factor theorem it is found that `a+b , b+ca n dc+a` are three factors of the determinant `|[-2a, a+b, a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|dot` The other factor in the value of the determinant is (a) 4 (b) 2 (c_ `a+b+c` (d) none of these

Explanation

Given,`|[-2a, a+b, a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|dot`

=`−2a(4b−(b+c)^2)−(a+b)[−2c(b+a)−(b+c)(c+a)]
+(a+c)[(b+a)(+b)+2b(a+c)]`


=`4(b+c)(c+a)(a+b)`


∴Other factor is 4