We have, p(x)=x4+x2+1 Using the formula: a4+a2+1=(a2−a+1)(a2+a+1) (a+b+c)2=a2+b2+c2+2ab+2bc+2ac ⇒p(x)=(x2−x+1)(x2+x+1)⋅⋅⋅⋅⋅⋅⋅(i) ⇒q(x)=x4−2x3+3x2−2x+1⋅⋅⋅⋅⋅⋅⋅(ii) Also, we have, (x2−x+1) By using the above formula ⇒(x2−x+1)2=x4+x2+1+2(−x)3+(−2x)+(2x2) ⇒(x2−x+1)2=x4+3x2−2x3−2x+1 Using equation (2) ⇒q(x)=(x2−x+1)2 Now we have two polynomial p(x)&q(x) By using the concept of LCM discussed above LCM=(x2+x+1)(x2−x+1)2 ∴ The required LCM is (x2+x+1)(x2−x+1)2