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

Question

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

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we first rewrite them so we can align like terms:

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

• \quad p^4 - 3p + 4 \]

Now, we can add the coefficients of each corresponding term:

1. The \(p^4\) term: \[0 + 1 = p^4\]
2. The \(p^2\) term: \[-5 + 0 = -5p^2\]
3. The \(p\) term: \[-2 - 3 = -5p\]
4. The constant terms: \[3 + 4 = 7\]

Putting this all together, we get:

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

Thus, the result of adding the two polynomials is:

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