If a2+b2+c2≠−2 andf(x)=∣∣∣∣∣(1+a2)x(1+a2)x(1+a2)x(1+b2)x(1+b2)x(1+b2)x(1+c2)x(1+c2)x(1+c2)x∣∣∣∣∣then f(x) is a polynomial of degree

[d] f(x)= ∣∣∣∣∣1+(a2+b2+c2+2)x1+(a2+b2+c2+2)x1+(a2+b2+c2+2)x(1+b2)x1+b2x(1+b2)x(1+c2)x(1+c2)x1+c2x∣∣∣∣∣ Applying, C1→C1+C2+C3 =∣∣∣∣∣111(1+b2)x1+b2x(1+b2)x(1+c2)x(1+c2)x1+c2x∣∣∣∣∣ ∴a2+b2+c2+2≠0 f(x)=∣∣∣∣∣001x−11−x(1+b2)x0x−11+c2x∣∣∣∣∣ Applying  R1→R1−R2, R2→R2−R3 f(x)=(x−1)2 Hence degree = 2.