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 can arrange and combine like terms.

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

2. **Combine like terms:**
- The \(p^4\) term: \(p^4\)
- The \(p^2\) term: \(-5p^2\)
- The \(p\) terms: \(-2p - 3p = -5p\)
- The constant terms: \(3 + 4 = 7\)

3. **Write the resulting polynomial with combined terms:**
\[
p^4 - 5p^2 - 5p + 7
\]

So, the sum of the polynomials \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\) is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]