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

Question

Responses

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

−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

Answer 1

To add the polynomials \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we align like terms:

1. Start with the polynomial expressions: \[ (3 - 2p - 5p^2) + (p^4 - 3p + 4) \]

2. Combine the terms:

   • The \(p^4\) term is from the second polynomial: \(p^4\)
   • The \(p^2\) term is from the first polynomial: \(-5p^2\)
   • The \(p\) terms are \(-2p\) and \(-3p\), which combine to \(-5p\)
   • The constant terms are \(3\) from the first polynomial and \(4\) from the second polynomial; together they sum to \(7\).

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

Thus, the resulting polynomial expression is: \[ \boxed{p^4 - 5p^2 - 5p + 7} \]

This matches the first response option provided: \(p^4 - 5p^2 - 5p + 7\).