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Which of the following is not a factor of the expression 3x³−75x ?

a) x
b)3x
c)5
d)15x

User Isabell
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1 Answer

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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.

User Shurdoof
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