Question

The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend? The choices are: A. 6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8 B. 6d5 – 4c3d2 + 3c2d3 – 4cd4 + 8 C. 6d5 – 4c3d2 + 5c2d3 – 12cd4 + 8 D. 6d5 – 2c3d2 – 3c2d3 – 4cd4 + 8

Answer 1

6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8

Answer 2

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.