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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we first write them together:
\[
3 - 2p - 5p^2 + p^4 - 3p + 4
\]
Now, we can combine like terms. Let's group them according to their degrees:
- For \(p^4\): \(p^4\)
- For \(p^2\): \(-5p^2\)
- For \(p\): \(-2p - 3p = -5p\)
- For the constant terms: \(3 + 4 = 7\)
Putting it all together, we have:
\[
p^4 - 5p^2 - 5p + 7
\]
Thus, the correct response is:
**\(p^4 - 5p^2 - 5p + 7\)**