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

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

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

p4−5p2−6p+7

Answer 1

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

1. First, write the polynomials in standard form (descending order of powers):
\[
-5p^2 - 2p + 3
\]
and
\[
p^4 - 3p + 4
\]

2. Now, line them up for addition:
\[
p^4 + (-5p^2) + (-2p) + 3
\]
\[
+ 0 + 0 - 3p + 4
\]

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

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

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