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 combine like terms. Here are the steps:

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

2. Align the like terms:
- The highest degree term is \(p^4\).
- The next degree term is \(-5p^2\).
- The linear terms are \(-2p\) and \(-3p\).
- The constant terms are \(3\) and \(4\).

3. Now, add the corresponding terms:
- \(p^4\) remains \(p^4\)
- \(-5p^2\) remains \(-5p^2\)
- \(-2p - 3p = -5p\)
- \(3 + 4 = 7\)

Putting all of this together, we get:

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

Thus, the sum of the two polynomials is:

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