If 4 x^3+16 x+7 (x^2+4 )^2 = A x+B x^2+4 + C x+D (x^2+4 )^2 , then the number of non-zero values in A, B, C, D is

Step-by-step solution

4 x^3+16 x+7 (x^2+4 )^2 = A x+B x^2+4 + C x+D (x^2+4 )^2 = (A x+B) (x^2+4 )+(C x+D) (x^2+4 )^2 aligned & 4 x^3+16 x+7=A x^3+B x^2+(4 A+C) x+(4 B+D) & A=4, B=0 4 A+C=16 & C=0 and 4 B+D=7 D=7 aligned The number of non-zero values in A, B, C and D=2