Add the polynomial expressions 3−2p−5p^2 and p^4−3p+4 .(1 point) Responses

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

1. **Write the polynomials in a standard form (descending powers of \( p \))**:
- First polynomial: \( -5p^2 - 2p + 3 \)
- Second polynomial: \( p^4 - 3p + 4 \)

2. **Align them for addition**:
\[
\begin{array}{r}
p^4 \\
- 5p^2 \\
- 2p \\
+ 3 \\
+ 4 \\
\end{array}
\]

3. **Combine like terms**:
- The \( p^4 \) term: \( 1p^4 \) (only from the second polynomial)
- The \( p^2 \) term: \( -5p^2 \) (only from the first polynomial)
- The \( p \) term: \( -2p - 3p = -5p \)
- The constant terms: \( 3 + 4 = 7 \)

4. **Combine all together**:
\[
p^4 - 5p^2 - 5p + 7
\]

So, the result of adding the polynomials \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \) is:

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