Answer: The correct option is A.
Step-by-step explanation: We are given a polynomial which is a sum of other 2 polynomials.
We are given the resultant polynomial which is : \(8d^5-3c^3d^2+5c^2d^3-4cd^4+9\)
One of the polynomial which are added up is : \(2d^5-c^3d^2+8cd^4+1\)
Let the other polynomial be 'x'
According to the question:
\(8d^5-3c^3d^2+5c^2d^3-4cd^4+9=x+(2d^5-c^3d^2+8cd^4+1)\)
\(x=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)\)
Solving the like terms in above equation we get:
\(x=(8d^5-2d^5)+(-3c^3d^2+c^3d^2)+(5c^2d^3)+(-4cd^4-8cd^4)+(9-1)\)
\(x=6d^5-2c^3d^2+5c^2d^3-12cd^4+8\)
Hence, the correct option is A.
