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

Responses

−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

p4−5p2−6p+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 \( p^4 - 3p + 4 \), we combine like terms.

1. Identify and list the terms from both polynomials:
- From \( 3 - 2p - 5p^2 \), we have:
- Constant: \( 3 \)
- Linear: \( -2p \)
- Quadratic: \( -5p^2 \)
- From \( p^4 - 3p + 4 \), we have:
- Constant: \( 4 \)
- Linear: \( -3p \)
- quartic: \( p^4 \)

2. Combine like terms:
- Quartic: \( p^4 \)
- Quadratic: \( -5p^2 \)
- Linear: \( -2p - 3p = -5p \)
- Constant: \( 3 + 4 = 7 \)

Putting it all together:
\[ p^4 - 5p^2 - 5p + 7 \]

So the result is:
\[ p^4 - 5p^2 - 5p + 7 \]

The correct response is:
**p4−5p2−5p+7**.