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

Question

Responses

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

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

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

−4p2−5p+7

Answer 1

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

1. Start with the first polynomial: \(3 - 2p - 5p^2\).
2. Add the second polynomial: \(p^4 - 3p + 4\).

Combining these gives:

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

Now, combine the terms:

• The \(p^4\) term remains \(p^4\).
• The \( -5p^2 \) term remains \( -5p^2\).
• Combine the \(p\) terms: \(-2p - 3p = -5p\).
• Combine the constant terms: \(3 + 4 = 7\).

So, the resulting polynomial expression is:

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

Thus, the correct response is:

p^4 - 5p^2 - 5p + 7.