Add the polynomial expressions 3−2p−5p^2 and p^4−3p+4 .

Question

A, p^4-5p^2-5p+7

B, -4p2-5p+7

C, -5p^2-4p+7

D, p^4-5p^2-6p+7

Answer 1

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

1. Start by writing the two polynomials vertically, aligning like terms:

   \[ \begin{array}{r} 3 \ -2p \ -5p^2 \

   • p^4 \ -3p \ +4 \ \end{array} \]

2. Now, add the polynomials term by term:

   • The \( p^4 \) term: \( 0 + p^4 = p^4 \)
   • The \( p^2 \) term: \( -5p^2 + 0 = -5p^2 \)
   • The \( p \) term: \( -2p - 3p = -5p \)
   • The constant term: \( 3 + 4 = 7 \)

3. Combine them together:

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

So the final result after adding the two polynomial expressions is:

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

Thus, the correct answer is:

A, \( p^4 - 5p^2 - 5p + 7 \).