Which one of the following statements is not correct ?

Options

A. `a^(2)+b^(2)` cannot be factorized
B. `(a-2c)` is a factor of `a^(2)-4a^(2)c^(2)`
C. `2x+7` is a factor of `8x^(3)-27`
D. `(3a^(2)-13a-10)/(9a^(2)-4)=(a-5)/(3a-2)`

Answer

To solve the problem of identifying which statement is not correct, we will analyze each of the four statements provided.

### Step-by-Step Solution:

1. **Statement A: \( a^2 + b^2 \) cannot be factorized.**
- This statement is **true**. The expression \( a^2 + b^2 \) cannot be factored into real numbers. It can only be expressed in terms of complex numbers or using identities, but it is not factorable in the traditional sense.

2. **Statement B: \( a - 2ac \) is a factor of \( a^2 - 4a^2c^2 \).**
- Let's analyze this statement:
- The expression \( a^2 - 4a^2c^2 \) can be rewritten as \( a^2(1 - 4c^2) \).
- This is a difference of squares, which can be factored as \( a^2(1 - 2c)(1 + 2c) \).
- Therefore, \( a - 2ac \) is not a factor of this expression. This statement is **false**.

3. **Statement C: \( 2x + 7 \) is a factor of \( 8x^3 - 27 \).**
- To check if \( 2x + 7 \) is a factor, we can use polynomial long division.
- Dividing \( 8x^3 - 27 \) by \( 2x + 7 \) gives us a remainder.
- Since the remainder is not zero, \( 2x + 7 \) is not a factor. This statement is **false**.

4. **Statement D: The expression \( \frac{3a^2 - 15a + 2a - 10}{9a^2 - 4} \) simplifies correctly.**
- Simplifying the numerator:
- Combine like terms: \( 3a^2 - 15a + 2a - 10 = 3a^2 - 13a - 10 \).
- The denominator \( 9a^2 - 4 \) is a difference of squares: \( (3a - 2)(3a + 2) \).
- After simplification, the expression holds true, making this statement **true**.

### Conclusion:
The incorrect statements are B and C. However, since the question asks for one statement that is not correct, we conclude that the answer is:

**Statement C: \( 2x + 7 \) is a factor of \( 8x^3 - 27 \) is not correct.**