Question

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

−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
negative 4 p squared minus 5 p plus 7

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

Answer 1

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

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

2. Add the second polynomial:
\(p^4 - 3p + 4\)

Now, combine them:

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

This simplifies to:

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

So, the resulting polynomial is:

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

The correct response is:

**p^4−5p^2−5p+7** (p superscript 4 baseline minus 5 p squared minus 5 p plus 7)