Question

Add the Polynomial expressions 3-2p-5p^2 and p^4-3p+4

Answer 1

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

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

2. Align the terms by their degree:
\[
p^4 + 0p^3 - 5p^2 - 2p + (3 + 4)
\]

3. Combine the constants and like terms:
- For \(p^4\), we have \(1p^4\).
- For \(p^3\), we have \(0p^3\).
- For \(p^2\), we have \(-5p^2\).
- For \(p\), we have \(-2p - 3p = -5p\).
- For the constant terms, \(3 + 4 = 7\).

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

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