Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .(1 point) Responses

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

1. Write down the two expressions:
\[
(3 - 2p - 5p^2) + (p^4 - 3p + 4)
\]

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

3. Combine these results:
\[
p^4 - 5p^2 - 5p + 7
\]

So, the resulting polynomial after addition is:
\[
p^4 - 5p^2 - 5p + 7
\]