To add the polynomial expressions \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \), we combine like terms.
1. Identify and list the terms from both polynomials:
- From \( 3 - 2p - 5p^2 \), we have:
- Constant: \( 3 \)
- Linear: \( -2p \)
- Quadratic: \( -5p^2 \)
- From \( p^4 - 3p + 4 \), we have:
- Constant: \( 4 \)
- Linear: \( -3p \)
- quartic: \( p^4 \)
2. Combine like terms:
- Quartic: \( p^4 \)
- Quadratic: \( -5p^2 \)
- Linear: \( -2p - 3p = -5p \)
- Constant: \( 3 + 4 = 7 \)
Putting it all together:
\[ p^4 - 5p^2 - 5p + 7 \]
So the result is:
\[ p^4 - 5p^2 - 5p + 7 \]
The correct response is:
**p4−5p2−5p+7**.