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

Answer 1

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

1. Write the polynomials in a standard form (descending powers of \( p \)):

   • First polynomial: \( -5p^2 - 2p + 3 \)
   • Second polynomial: \( p^4 - 3p + 4 \)

2. Align them for addition: \[ \begin{array}{r} p^4 \

   • 5p^2 \
   • 2p \
   • 3 \
   • 4 \ \end{array} \]

3. Combine like terms:

   • The \( p^4 \) term: \( 1p^4 \) (only from the second polynomial)
   • The \( p^2 \) term: \( -5p^2 \) (only from the first polynomial)
   • The \( p \) term: \( -2p - 3p = -5p \)
   • The constant terms: \( 3 + 4 = 7 \)

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

So, the result of adding the polynomials \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \) is:

\[ \boxed{p^4 - 5p^2 - 5p + 7} \]