Add the polynomial expressions 3−2p−5p^2 and p^4−3p+4.

Question

Responses:
p^4−5p^2−5p+7
p^4−5p^2−6p+7
−5p^2−4p+7
−4p^2−5p+7

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms step by step.

1. Write down both expressions: \[ 3 - 2p - 5p^2 \] \[

   • \ (p^4 - 3p + 4) \]

2. Group the terms by their degree:

   • \(p^4\)
   • \(p^2\)
   • \(p\)
   • constant

3. Now, combine the like terms:

   • The \(p^4\) term: \(p^4\)
   • The \(p^2\) term: \(-5p^2\)
   • The \(p\) terms: \(-2p - 3p = -5p\)
   • The constant terms: \(3 + 4 = 7\)

Putting these together, we have: \[ p^4 - 5p^2 - 5p + 7 \]

Thus, the final result is: \[ \boxed{p^4 - 5p^2 - 5p + 7} \]