In the method of factorisation of an algebraic expression, which of the following statement is false ?

Options

A. Taking out a common factor from two or more terms .
B. Taking out a common factor from a group of terms .
C. Using remainder theorem .
D. Using standard identities .

Answer

To determine which statement is false regarding the methods of factorization of an algebraic expression, we will analyze each option based on the methods used in factorization.

### Step-by-Step Solution:

1. **Identify the Statements**:
The statements provided are:
- (1) Taking out a common factor from two or more terms.
- (2) Taking out a common factor from a group of terms.
- (3) Using the remainder theorem.
- (4) Using standard identities.

2. **Analyze Each Statement**:
- **Statement 1**: Taking out a common factor from two or more terms.
- In the example \(x^2 + 8x + 16\), we can factor out common terms. This method was used when we factored \(x^2 + 4x + 4x + 16\) into groups. This statement is **true**.

- **Statement 2**: Taking out a common factor from a group of terms.
- Similar to statement 1, we grouped terms and factored out common factors. This was also used in the factorization process. This statement is **true**.

- **Statement 3**: Using the remainder theorem.
- The remainder theorem is not applicable in this context of factorization for the given polynomial. We did not use the remainder theorem in our factorization process. This statement is **false**.

- **Statement 4**: Using standard identities.
- The expression \(x^2 + 8x + 16\) can be recognized as a perfect square, which is a standard identity. We used this identity to factor the expression. This statement is **true**.

3. **Conclusion**:
The false statement among the options is **Statement 3: Using the remainder theorem**.

### Final Answer:
The false statement is: **Using the remainder theorem**.