Question

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
negative 4 p squared minus 5 p plus 7

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms.

1. **Arrange the terms**:
- From \(3 - 2p - 5p^2\), we have:
- \(3\) (constant term)
- \(-2p\) (linear term)
- \(-5p^2\) (quadratic term)
- From \(p^4 - 3p + 4\), we have:
- \(p^4\) (quartic term)
- \(-3p\) (linear term)
- \(4\) (constant term)

2. **Combine the polynomials**:
- The quartic term: \(p^4\)
- The quadratic term: \(-5p^2\)
- The linear terms: \(-2p - 3p = -5p\)
- The constant terms: \(3 + 4 = 7\)

3. **Putting it all together**:
The resulting polynomial is:
\[
p^4 - 5p^2 - 5p + 7
\]

Thus, the correct answer is:
**\(p^4 - 5p^2 - 5p + 7\)**.