Question

Add the polynomial expressions 3−2p−5p2 and p4−3p+4.(1 point)%0D%0AResponses%0D%0A%0D%0A−4p2−5p+7%0D%0Anegative 4 p squared minus 5 p plus 7%0D%0A%0D%0Ap4−5p2−6p+7%0D%0Ap superscript 4 baseline minus 5 p squared minus 6 p plus 7%0D%0A%0D%0Ap4−5p2−5p+7%0D%0Ap superscript 4 baseline minus 5 p squared minus 5 p plus 7%0D%0A%0D%0A−5p2−4p+7

Answer 1

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

1. Start by rewriting both polynomials: \[ (3 - 2p - 5p^2) + (p^4 - 3p + 4) \]

2. Rearranging the terms, we get: \[ p^4 - 5p^2 + (-2p - 3p) + (3 + 4) \]

3. Now, combine the like terms:

   • The \(p^4\) term remains \(p^4\).
   • The \(p^2\) term is \(-5p^2\).
   • For the \(p\) terms, \(-2p - 3p = -5p\).
   • The constant terms \(3 + 4 = 7\).

4. Putting it all together: \[ p^4 - 5p^2 - 5p + 7 \]

Therefore, the final result is: \[ p^4 - 5p^2 - 5p + 7 \]

So the correct response is: \[ \text{ } p^4 - 5p^2 - 5p + 7 \]