Final answer:
The expression 3x³−75x factors to 3x(x² − 25), which further factors into 3x(x − 5)(x + 5). The options x, 3x, and 5 are factors or part of the factors of the expression, while 15x is not a stand-alone factor.
Hence, 15x is not a factor of the given expression.
Step-by-step explanation:
To determine which of the given options is not a factor of the expression 3x³−75x, we first need to factor the expression completely. Factoring out the greatest common factor (GCF), which is 3x, we get:
3x(x² − 25) = 3x(x − 5)(x + 5)
Now that the expression is fully factored, we can see that the factors of 3x³−75x are 3x, (x − 5), and (x + 5). Thus, the options given can be evaluated as follows:
- a) x - Yes, x is a part of the first factor 3x.
- b) 3x - Yes, 3x is the GCF that we factored out.
- c) 5 - Not directly, but 5 is a part of the factors (x − 5) and (x + 5).
- d) 15x - No, 15x is not a factor of the given expression because when you factor it, 15x does not appear as a stand-alone factor.
Therefore, the option that is not a factor of the expression 3x³−75x is d) 15x.