Add the polynomial expressions 3 - 2p - 5p ^ 2 and p ^ 4 - 3p + 4 (1 point) p ^ 4 - 5p ^ 2 - 6p + 7; - 4p ^ 2 - 5p + 7; p ^ 4 - 5p ^ 2 - 5p + 7; - 5p ^ 2 - 4p + 7

Answer 1

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

1. Rewrite both polynomials:

   \[ 3 - 2p - 5p^2 \] \[ p^4 - 3p + 4 \]

2. Arrange them as follows:

   \[ (p^4) + (0p^3) + (-5p^2) + (-2p) + (3) + (4) + (-3p) \]

3. Now combine them:

   • The \(p^4\) term: \(p^4\)
   • The \(p^3\) term: \(0p^3\) (no \(p^3\) in either polynomial)
   • The \(p^2\) term: \(-5p^2\)
   • The \(p\) terms: \(-2p - 3p = -5p\)
   • The constant terms: \(3 + 4 = 7\)

4. Putting it all together, we have:

   \[ p^4 + 0p^3 - 5p^2 - 5p + 7 \]

5. Drop the zero coefficient for \(p^3\):

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

So the final result is:

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

From the options you provided, the corresponding answer is:

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