Add the polynomial expressions 3−2p−5p^2 and p^4−3p+4 .

To add the polynomial expressions \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \), you need to combine like terms:

1. Write the two polynomials one under the other, aligning like terms:

\[
\begin{array}{r}
3 \\
-2p \\
-5p^2 \\
\hline
\end{array}
+
\begin{array}{r}
p^4 \\
-3p \\
4 \\
\hline
\end{array}
\]

2. Now, combine all the like terms:

- The highest degree term is \( p^4 \).
- The \( p^2 \) term is \( -5p^2 \).
- The \( p \) terms are \( -2p - 3p = -5p \).
- The constant terms are \( 3 + 4 = 7 \).

Putting it all together, we get:

\[
p^4 - 5p^2 - 5p + 7
\]

Thus, the sum of the polynomials \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \) is:

\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]