Q.8 see image.........................................................................

consider the determinant as a polynomial function in a, p(a), assuming b and c are constants.

then det= p(a)

now, p(a=b)= p(b) = 0 because first and second rows become identical on replacing a by b.

by factor theorem, p(a) must be divisible by a – b.

similarly of you consider the determinant as a polynomial function in b, f(b), assuming a and c as constants, then find f(c), it will be zero implying divisibility by b – c.

and similarly consider the determinant as a polynomial function in c, g(c), assuming b and a are constants. g(a)=0 hence divisible by c – a.