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 can combine like terms.

1. Start by rewriting both expressions:

\[
3 - 2p - 5p^2 \quad (1)
\]
\[
p^4 - 3p + 4 \quad (2)
\]

2. Now, let's align them for addition:

\[
0p^4 + 0p^3 - 5p^2 - 2p + 3 \quad (from \; expression \; 1)
\]
\[
+1p^4 + 0p^3 + 0p^2 - 3p + 4 \quad (from \; expression \; 2)
\]

3. Adding these together term by term gives us:

- For \(p^4\): \(0 + 1 = 1\)
- For \(p^3\): \(0 + 0 = 0\)
- For \(p^2\): \(-5 + 0 = -5\)
- For \(p\): \(-2 - 3 = -5\)
- For the constant terms: \(3 + 4 = 7\)

4. So the result of the addition is:

\[
p^4 + 0p^3 - 5p^2 - 5p + 7
\]

5. This simplifies to:

\[
p^4 - 5p^2 - 5p + 7
\]

So the answer is:

\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]