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