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

Answer 1

To add the polynomial expressions \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \), we first align the terms by their degrees:

1. Write down the polynomials:
- First polynomial: \( 3 - 2p - 5p^2 \)
- Second polynomial: \( p^4 - 3p + 4 \)

2. Rearrange them for addition:
\[
-5p^2 - 2p + 3
\]
\[
+ p^4 - 3p + 4
\]

3. Now add them by combining like terms:
- The \( p^4 \) term: \( 1p^4 \)
- The \( p^2 \) term: \( -5p^2 \)
- The \( p \) terms: \( -2p - 3p = -5p \)
- The constant terms: \( 3 + 4 = 7 \)

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

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