To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we first need to rearrange them by their degree:
1. \(p^4 - 3p + 4\)
2. \( - 5p^2 - 2p + 3\)
Now, we perform the addition term by term:
- For \(p^4\), we have:
\[
p^4
\]
- For \(p^3\), there are no \(p^3\) terms in either polynomial, so it contributes:
\[
0
\]
- For \(p^2\), we have:
\[
-5p^2
\]
- For \(p^1\), we combine:
\[
-2p - 3p = -5p
\]
- For the constant term, we combine:
\[
4 + 3 = 7
\]
Putting it all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]
The correct response is:
**\(p^4 - 5p^2 - 5p + 7\)**.