Final answer:
The expression 3x³ - 75x can be factored into 3x(x + 5)(x - 5) and thus, the factors are 3x, x + 5, and x - 5. The provided option C) x + 3 is not included in the factored form and therefore is not a factor of the given expression.
Step-by-step explanation:
The expression given is 3x³ - 75x. To determine which of the provided options is not a factor, we need to look at whether each option can divide the expression without leaving a remainder. We can start by factoring out the greatest common factor (GCF) which is 3x. The expression becomes 3x(x² - 25). The term (x² - 25) is a difference of squares and can be factored further into (x + 5)(x - 5). Therefore, the factors of the expression are 3x, x + 5, and x - 5. Looking at the options provided:
- A) x + 5 is a factor, as we have just established.
- B) 3x is a factor, because it's the GCF we factored out first.
- D) x² - 25 is a factor, as it is equivalent to (x + 5)(x - 5).
- C) x + 3 does not appear in any of our factored forms, so it is not a factor.
Therefore, the option that is not a factor of the expression 3x³ - 75x is C) x + 3.