Question

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

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we first align the like terms from each expression:

1. \(p^4\)
2. \(-5p^2\)
3. \(-2p\) and \(-3p\)
4. Constant terms \(3\) and \(4\)

Now, we can add them together:

1. The highest degree term: \(p^4\)
2. The next term: \(-5p^2\)
3. Combining the \(p\) terms: \(-2p - 3p = -5p\)
4. Combining the constant terms: \(3 + 4 = 7\)

Putting it all together, we have:

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

Thus, the correct response is:

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