To add the polynomial expressions \(3 - 2p - 5p^2 + p^4 - 3p + 4\), we start by combining like terms.
- Constant terms: \(3 + 4 = 7\)
- Linear terms: \(-2p - 3p = -5p\)
- Quadratic terms: \(-5p^2\) (there’s no other \(p^2\) term)
- Quartic term: \(p^4\) (there’s no other \(p^4\) term)
Now, we can write the final expression by putting all like terms together:
\[ p^4 - 5p^2 - 5p + 7 \]
So, the sum of the polynomial expressions is:
\[ p^4 - 5p^2 - 5p + 7 \]