Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .(1 point) Responses

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), you align the like terms as follows:

1. Write down the two expressions: \[ (3 - 2p - 5p^2) + (p^4 - 3p + 4) \]

2. Combine like terms:

   • The constant terms: \(3 + 4 = 7\)
   • The linear terms (with \(p\)): \(-2p - 3p = -5p\)
   • The quadratic term (with \(p^2\)): only \(-5p^2\) from the first polynomial
   • The quartic term (with \(p^4\)): only \(p^4\) from the second polynomial

3. Combine these results: \[ p^4 - 5p^2 - 5p + 7 \]

So, the resulting polynomial after addition is: \[ p^4 - 5p^2 - 5p + 7 \]