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

−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

−5p2−4p+7

Answer 1

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

1. Write down both polynomials:
\[
3 - 2p - 5p^2
\]
\[
p^4 - 3p + 4
\]

2. Rewrite them aligning the terms:
\[
p^4 + 0 \cdot p^3 - 5p^2 - 2p + 3
\]
\[
0 \cdot p^4 + 0 \cdot p^3 - 5p^2 - 3p + 4
\]

3. Now, add the corresponding coefficients:
- The \(p^4\) term: \(1\) (from \(p^4\))
- The \(p^3\) term: \(0\)
- The \(p^2\) term: \(-5 + 0 = -5\)
- The \(p\) term: \(-2 - 3 = -5\)
- The constant term: \(3 + 4 = 7\)

4. Combine these to get the final polynomial:
\[
p^4 - 5p^2 - 5p + 7
\]

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