Question

Find the sum. (4p−2p2+8)+(5p2+2p)+(7−3p)
(1 point)
Responses

−2p2+8p+15
negative 2 p squared plus 8 p plus 15

3p2+3p+15
3 p squared plus 3 p plus 15

3p2+6p+15
3 p squared plus 6 p plus 15

5p2+p+15

Answer 1

To find the sum of the expressions \((4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)\), we will combine like terms.

1. First, let's rewrite the expressions:

\[
(4p - 2p^2 + 8)
\]
\[
+ (5p^2 + 2p)
\]
\[
+ (7 - 3p)
\]

2. Now, we'll group the like terms (the terms with \(p^2\), the terms with \(p\), and the constant terms):

- \(p^2\) terms: \(-2p^2 + 5p^2\)
- \(p\) terms: \(4p + 2p - 3p\)
- Constant terms: \(8 + 7\)

3. Now, we sum each group:

- For \(p^2\) terms:
\(-2p^2 + 5p^2 = 3p^2\)

- For \(p\) terms:
\(4p + 2p - 3p = 3p\)

- For constant terms:
\(8 + 7 = 15\)

4. Combining all results, we get:

\[
3p^2 + 3p + 15
\]

Therefore, the final answer is:

**3p² + 3p + 15** (which corresponds to the second response option).