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

Responses

p4−5p2−5p+7
p superscript 4 baseline minus 5 p squared minus 5 p plus 7

p4−5p2−6p+7
p superscript 4 baseline minus 5 p squared minus 6 p plus 7

−5p2−4p+7
negative 5 p squared minus 4 p plus 7

−4p2−5p+7
negative 4 p squared minus 5 p plus 7

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we first write them together:

\[
3 - 2p - 5p^2 + p^4 - 3p + 4
\]

Now, we can combine like terms. Let's group them according to their degrees:

- For \(p^4\): \(p^4\)
- For \(p^2\): \(-5p^2\)
- For \(p\): \(-2p - 3p = -5p\)
- For the constant terms: \(3 + 4 = 7\)

Putting it all together, we have:

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

Thus, the correct response is:

**\(p^4 - 5p^2 - 5p + 7\)**