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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms.
1. Rewrite both polynomials:
\[
3 - 2p - 5p^2
\]
\[
p^4 - 3p + 4
\]
2. Arrange them as follows:
\[
(p^4) + (0p^3) + (-5p^2) + (-2p) + (3) + (4) + (-3p)
\]
3. Now combine them:
- The \(p^4\) term: \(p^4\)
- The \(p^3\) term: \(0p^3\) (no \(p^3\) in either polynomial)
- The \(p^2\) term: \(-5p^2\)
- The \(p\) terms: \(-2p - 3p = -5p\)
- The constant terms: \(3 + 4 = 7\)
4. Putting it all together, we have:
\[
p^4 + 0p^3 - 5p^2 - 5p + 7
\]
5. Drop the zero coefficient for \(p^3\):
\[
p^4 - 5p^2 - 5p + 7
\]
So the final result is:
\[
p^4 - 5p^2 - 5p + 7
\]
From the options you provided, the corresponding answer is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]