Question

Explain in words how to add the polynomial 5p^3+2p-1 and 2p^2+8p+6

Answer 1

`5p^3+2p^2+10p+5`

Explanation:

We have the following polynomial expressions

`5p^3+2p-1` and
`2p^2+8p+6`

To make the sum of both expressions you must add the terms that have the same variable and the same exponent

`5p^3+0p^3=5p^3\\\\2p^2+0p^2=2p^2\\\\2p+8p = 10p\\\\-1+6=5`

Finally the sum of the polynomials is:

`5p^3+2p^2+10p+5`

Answer 2

For this case we have the following polynomials:

`5p ^ 3 + 2p-1\\2p ^ 2 + 8p + 6`

To add the polynomials we must add term by term according to the degree, that is, add similar terms:

`5p ^ 3 + 2p ^ 2 + (2 + 8) p + (- 1 + 6) = 5p ^ 3 + 2p ^ 2 + 10p + 5`

The first polynomial has a cubic term and the second does not, so the sum will have only the cubic term of the first polynomial. The same applies to the quadratic term of the second polynomial.

Answer:
`5p ^ 3 + 2p ^ 2 + 10p + 5`