To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms:
1. Start with the two polynomials:
- \(3 - 2p - 5p^2\)
- \(p^4 - 3p + 4\)
2. Arrange the terms by their degrees:
- \(p^4 + 0p^3 - 5p^2 + (-2p - 3p) + (3 + 4)\)
3. Perform the addition for each type of term:
- For \(p^4\): \(1\)
- For \(p^3\): \(0\)
- For \(p^2\): \(-5\)
- For \(p\): \(-2 - 3 = -5\)
- For the constant: \(3 + 4 = 7\)
Putting it all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]
The correct response is:
**\(p^4 - 5p^2 - 5p + 7\)** (or in the second response format: \(p \text{ superscript } 4 \text{ baseline } - 5 p^2 - 5 p + 7\)).