Add the Polynomial expressions 3-2p-5p^2 and p^4-3p+4

Question

A.-4p^2-5p+7
B. p^4-5p^2-5p+7
C. p^4-5p^2-6p+7
D. -5p^2-4p+7

Answer 1

To add the polynomial expressions \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \), we first write them together:

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

Next, we can rearrange the terms by their degrees:

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

Now, combine like terms:

1. The \( p^4 \) term is: \( p^4 \)
2. The \( p^2 \) term is: \( -5p^2 \)
3. The \( p \) terms are: \( -2p - 3p = -5p \)
4. The constant terms are: \( 3 + 4 = 7 \)

Putting it all together, we get:

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

Thus, the final result of the addition is:

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