add the polynomial expression 3 - 2p - 5p^2 and p^4 - 3p + 4

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we simply combine like terms.

1. Start with the first polynomial: \[ 3 - 2p - 5p^2 \]

2. Add the second polynomial: \[

   • (p^4 - 3p + 4) \]

3. Combine like terms:

   • The \(p^4\) term: \(p^4\)
   • The \(p^2\) term: \(-5p^2\)
   • The \(p\) terms: \(-2p - 3p = -5p\)
   • The constant terms: \(3 + 4 = 7\)

Putting it all together, we have: \[ p^4 - 5p^2 - 5p + 7 \]

So, the sum of the polynomials is: \[ \boxed{p^4 - 5p^2 - 5p + 7} \]