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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we combine like terms.
1. Write down both polynomials:
\[
3 - 2p - 5p^2
\]
\[
p^4 - 3p + 4
\]
2. Combine them into one expression:
\[
3 - 2p - 5p^2 + p^4 - 3p + 4
\]
3. Rearrange and group like terms:
\[
p^4 + (-5p^2) + (-2p - 3p) + (3 + 4)
\]
4. Combine the coefficients:
- For \(p^4\): just \(p^4\)
- For \(p^2\): \(-5p^2\)
- For \(p\): \(-2p - 3p = -5p\)
- Constant: \(3 + 4 = 7\)
5. Putting it all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]
So the answer is:
**D**: \(p^4 - 5p^2 - 5p + 7\)