aligned & If x+2 (x^2+3 ) (x^4+x^2 ) (x^2+2 ) = A x+B x^2+3 + C x+D x^2+2 + & E x^3+F x^2+G x+H x^4+x^2 then (E + F) (C + D) (A) = aligned

Step-by-step solution

aligned & x+2 (x^2+3 ) (x^4+x^2 ) (x^2+2 ) & = A^ x + B^ x^2 + C^ x+D^ x^2+1 + E^ x+F^ x^2+2 + G^ x+H^ x^2+3 & x+2=x (x^2+1 ) (x^2+2 ) (x^2+3 ) A^ & + (x^2+1 ) (x^2+2 ) (x^2+3 ) B^ + (C^ x+D ) x^2 (x^2+2 ) & (x^2+3 ) +x^2 (x^2+1 ) (x^2+3 ) (E^ x+F^ )+x^2 (x^2+1 ) (x^2+ . & 2) (G^ x+H^ ) aligned aligned & x+2=x^7 (A^ +C^ +E^ +G^ )+x^6 (B^ +D^ +F^ +G^ ) & +x^5 (6 A^ +5 C^ +4 E^ +3 G^ )+x^4 (6 B^ +5 D^ +4 F^ +3 H^ )+x^3 & (11 A^ +6 C^ +3 E^ +2 G^ )+x^2(11 B+6 D+3 F+2 H)+6 x A+6 B aligned On comparing coefficients alig