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?

Answer 1

The another addend of the given polynomial is 6d^5 -2c^3d^2  + 5c^2d^3 - 12cd^4 + 8.

According to the given question.

We have a polynomial.

8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9

And, the one addend of the above polynomial is 2d^5 - c^3d^2 +8cd^4 + 1

Let the another addend of the given polynomial be x.

Then,

8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9  = x + 2d^5 - c^3d^2 +8cd^4 + 1

⇒ 8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9  - (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 = x

⇒6d^5 -2c^3d^2  + 5c^2d^3 - 12cd^4 + 8 = x

Hence, the another addend of the given polynomial is 6d^5 -2c^3d^2  + 5c^2d^3 - 12cd^4 + 8.

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