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

Responses

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

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

−4p2−5p+7

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), follow these steps:

1. Write the polynomials:

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

2. Group the like terms:

- Constant terms: \(3 + 4 = 7\)
- \(p\) terms: \(-2p - 3p = -5p\)
- \(p^2\) terms: \(-5p^2\)
- \(p^4\) term: \(p^4\)

3. Combine the results:

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

Therefore, the answer is:

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

This matches the response option:

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