32-bit representation refers to the number of bits used to represent a value in a computer system. In this case, it means that a 32-bit representation can have a total of 32 bits, which can be either 0 or 1.

The scale factor in a 32-bit representation refers to the range of values that can be represented using those 32 bits. It determines the minimum and maximum values that can be stored.

To determine the range of the scale factor in a 32-bit representation, we need to consider the number of bits allocated for the sign, exponent, and mantissa.

- Sign Bit: The sign bit represents the sign of the number, whether it is positive or negative. In a 32-bit representation, 1 bit is allocated for the sign. Therefore, the sign bit can be either 0 or 1, representing positive or negative values respectively.

- Exponent Bits: The exponent bits represent the magnitude of the number. In a 32-bit representation, typically 8 bits are allocated for the exponent. These bits can represent values from 0 to 255.

- Mantissa Bits: The mantissa bits represent the precision or fractional part of the number. In a 32-bit representation, typically 23 bits are allocated for the mantissa. These bits can represent values from 0 to 2^23 - 1.

Considering the above allocations, the range of the scale factor in a 32-bit representation can be calculated as follows:

- The range of the exponent is from 0 to 255, which corresponds to the scale factor of 2^0 to 2^255.

- The range of the mantissa is from 0 to 2^23 - 1, which corresponds to the scale factor of 2^0 to 2^(2^23 - 1).

However, it is important to note that the scale factor also includes the sign bit. Therefore, the overall range of the scale factor in a 32-bit representation is from -2^31 to 2^31 - 1, which corresponds to -2147483648 to 2147483647.

Hence, the correct answer is option A, which states that the scale factor in a 32-bit representation ranges from -128 to 127.