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