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

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

GPT-4o mini · Answer

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).