The determinant Δ= ∣∣
∣
∣∣a2+xabacabb2+xbcacbcc2+x∣∣
∣
∣∣ is divisible by
△=∣∣ ∣ ∣∣a2+xabacabb2+xbcacbcc2+x∣∣ ∣ ∣∣
(a2+x)(b2c2+b2x+c2x+x2−bx2)−ab(abc2+ab2−ab2)+ac(ab2c−acb2−acx)
a2x2+b2x2+c2x2+x3
(a2+b2+c2)x2+x3
x2(a2+b2+c2+x)
∴ Determinant is divisible by x2
also divisible by x.