Add the polynomial expressions 3−2p−5p2

Question

and p4−3p+4
.(1 point)
Responses

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

−5p2−4p+7
negative 5 p squared minus 4 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 can write them out together and combine like terms:

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

2. Combine the constants, the \( p \) terms, the \( p^2 \) terms, and the \( p^4 \) term:

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

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

Thus, the final result of adding the two polynomials is:

\[ p^4 - 5p^2 - 5p + 7 \]

From the options given, the correct response is:

\( p^4 - 5p^2 - 5p + 7 \)