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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), follow these steps:
1. Write the polynomials:
\[
(3 - 2p - 5p^2) + (p^4 - 3p + 4)
\]
2. Group the like terms:
- Constant terms: \(3 + 4 = 7\)
- \(p\) terms: \(-2p - 3p = -5p\)
- \(p^2\) terms: \(-5p^2\)
- \(p^4\) term: \(p^4\)
3. Combine the results:
\[
p^4 - 5p^2 - 5p + 7
\]
Therefore, the answer is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]
This matches the response option:
- \(p^4 - 5p^2 - 5p + 7\)