Question

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 to the 4th power 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

Answer 1

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

1. Write down the expressions:
\[
(3 - 2p - 5p^2) + (p^4 - 3p + 4)
\]

2. Combine the like terms:
- The constant terms are \(3\) and \(4\):
\[
3 + 4 = 7
\]
- The linear terms are \(-2p\) and \(-3p\):
\[
-2p - 3p = -5p
\]
- The quadratic term is \(-5p^2\).
- The quartic term is \(p^4\).

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

Thus, the result is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]