1 answer
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To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we combine like terms.
1. Start with the first polynomial:
\[
3 - 2p - 5p^2
\]
2. Now, add the second polynomial:
\[
+ (p^4 - 3p + 4)
\]
3. Combine 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 this all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]
The final answer is:
\[
p^4 - 5p^2 - 5p + 7
\]
So the correct response from the given options is:
\[
p^4 - 5p^2 - 5p + 7
\]