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

Question

Responses

−5p2−4p+7
negative 5 p squared minus 4 p plus 7

−4p2−5p+7
negative 4 p squared minus 5 p plus 7

p4−5p2−6p+7
p superscript 4 baseline minus 5 p squared minus 6 p plus 7

p4−5p2−5p+7

Answer 1

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

1. Start with the expression: \[ 3 - 2p - 5p^2 + p^4 - 3p + 4 \]

2. Now, rearranging and combining 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 it all together, we get: \[ p^4 - 5p^2 - 5p + 7 \]

Thus, the final answer is: \(p^4 - 5p^2 - 5p + 7\).