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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine the like terms.
1. Start with the expression:
\[
3 - 2p - 5p^2 + p^4 - 3p + 4
\]
2. Now, rearranging and combining 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 get:
\[
p^4 - 5p^2 - 5p + 7
\]
Thus, the final answer is:
**\(p^4 - 5p^2 - 5p + 7\)**.