To simplify the given expression $-3c + c^2 - 2 + c^2 + 5c + 3$, we need to combine like terms. Here's the step-by-step process:

1. Combine the $c^2$ terms:

   • $c^2 + c^2 = 2c^2$

2. Combine the $c$ terms:

   • $-3c + 5c = 2c$

3. Combine the constant terms:

   • $-2 + 3 = 1$

Thus, the simplified expression is: $2c^2 + 2c + 1$

Do you need further details or have any questions?

Related Questions:

1. How do you simplify expressions with higher powers, like $c^3$?
2. What happens if there are no like terms in an expression?
3. Can you explain how to factor the expression $2c^2 + 2c + 1$?
4. How do we simplify expressions with fractions or decimal coefficients?
5. What is the process for solving quadratic equations like $2c^2 + 2c + 1 = 0$?

Tip:

Always group similar terms together (like powers of $c$) before simplifying to avoid errors.