To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p - 3p + 4\), letβs first rewrite the second polynomial in a clearer form.
1. Combine the terms in the second polynomial:
\[
p - 3p + 4 = -2p + 4.
\]
Now we will add the two polynomials together:
2. Combine \(3 - 2p - 5p^2\) and \(-2p + 4\):
\[
(3 + 4) + (-2p - 2p) - 5p^2.
\]
3. Combine the constant terms, linear terms, and the quadratic term:
- Constant: \(3 + 4 = 7\),
- Linear: \(-2p - 2p = -4p\),
- Quadratic: \(-5p^2\).
Putting it all together, we get:
\[
-5p^2 - 4p + 7.
\]
Thus, the result of adding the two polynomial expressions is:
\[
-5p^2 - 4p + 7.
\]
So the correct answer is:
\[
0 - 5p^2 - 4p + 7.
\]
(Note that \(0 - 5p^2\) is just \(-5p^2\), so you can also represent it as \(-5p^2 - 4p + 7\)).