Question

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

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
negative 4 p squared minus 5 p plus 7

p4−5p2−5p+7

Answer 1

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

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

2. Combine the constant terms:
\[
3 + 4 = 7
\]

3. Combine the linear terms:
\[
-2p - 3p = -5p
\]

4. The quadratic term is:
\[
-5p^2
\]

5. The quartic term is:
\[
p^4
\]

Now, putting it all together, the resulting polynomial is:
\[
p^4 - 5p^2 - 5p + 7
\]

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

Among the given options:
- **p^4 - 5p^2 - 5p + 7** is the correct answer.