To determine the total surface area of the solar panels the agriculture club owns after Jessica completes the new chicken coop, we'll add the given surface area of the existing solar panels and the new solar panels on the chicken coop.
1. Identify the polynomials representing the surface areas:
- The surface area of the existing solar panel is given by:
[tex]\[
8c^2 + 16c - 11
\][/tex]
- The surface area of the new chicken coop solar panel is given by:
[tex]\[
28c^3 + 23c^2 - 15c
\][/tex]
2. Add the two polynomials together to find the total surface area:
[tex]\[
\left(8c^2 + 16c - 11\right) + \left(28c^3 + 23c^2 - 15c\right)
\][/tex]
3. Combine like terms:
- [tex]\( c^3 \)[/tex] terms: [tex]\( 28c^3 \)[/tex]
- [tex]\( c^2 \)[/tex] terms: [tex]\( 8c^2 + 23c^2 = 31c^2 \)[/tex]
- [tex]\( c \)[/tex] terms: [tex]\( 16c - 15c = c \)[/tex]
- Constant term: [tex]\( -11 \)[/tex]
Adding these together:
[tex]\[
28c^3 + 31c^2 + c - 11
\][/tex]
4. Verify this against the given options:
The total surface area of the solar panels is:
[tex]\[
28c^3 + 31c^2 + c - 11
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
28c^3 + 31c^2 + c - 11
\][/tex]
