To simplify the expression \( 8c - 2c^3 - 12 - 3c^2 \), we can combine like terms. Here are the steps:
Rearrange the terms in descending order of the powers of \( c \): \[ -2c^3 - 3c^2 + 8c - 12 \]
Identify the like terms:
- The term with \( c^3 \) is \( -2c^3 \).
- The term with \( c^2 \) is \( -3c^2 \).
- The term with \( c \) is \( 8c \).
- The constant term is \( -12 \).
Since there are no like terms to combine, we keep the expression as: \[ -2c^3 - 3c^2 + 8c - 12 \]
The simplified expression is: \[ -2c^3 - 3c^2 + 8c - 12 \]