Your parentheses are wrong in several places. Proper indentation can make these errors more clear:

    IF(
        CONTAINS(
            "Re-Admit...",
            LastName // <-- remove TEXT(...) call if this is a text field
        ), // <-- missing closing parenthesis added
        1, // <-- if your return type is Number, don't wrap the return value in quotes
        IF(
            CONTAINS(
                "Re-Admit 2...",
                LastName // <-- remove TEXT(...) call if this is a text field
            ), // <-- missing closing parenthesis added
            2, // <-- extra closing parenthesis removed
            // ^^^ if your return type is Number, don't wrap the return value in quotes
            IF(
                CONTAINS(
                    "Re-Admit 3...",
                    LastName // <-- remove TEXT(...) call if this is a text field
                ), // <-- missing closing parenthesis added
                3, // <-- extra closing parenthesis removed
                // ^^^ if your return type is Number, don't wrap the return value in quotes
                0 // <-- if your return type is Number, your fallback value should be 0 or null
            ) // <-- close third IF formula
        ) // <-- close second IF formula (added)
    ) // <-- close first IF formula (added)

I believe the first `CONTAINS` check will actually catch all the values from the subsequent checks, so you should also reverse the order, checking the `"1"` case last.

---

After reviewing the comments, nearly every single clause you implement has an error. It may be more legible to list them here:

- Your `IF` syntax needs to be `IF(logical_test, value_if_true, value_if_false)`.
- Your `CONTAINS` syntax needs to be `CONTAINS(text, compare_text)`.
- Composing these functions should yield `IF(CONTAINS(text, compare_text), value_if_true, value_if_false)`
- Composing three nested `IF` statements should yield `IF(condition1, value_if_condition1, IF(condition2, value_if_condition2, IF(condition3, value_if_condition3)))`
- You can't call `TEXT` on a field that is already of the type Text.
- To return a number, use values like `1` instead of `"1"`.
- The value `""` is not a valid number. Use `0` or `null` instead.