Question

Melany was asked to create an equivalent form of the rational expression  −3x2−15x−18x+3 . Which of the following is a correct equivalent form?(1 point)Responses−3x−6negative 3 x minus 6−3x−114negative 3 x minus 114This rational expression does not have any equivalent forms.This rational expression does not have any equivalent forms.−3x−24−114x+3negative 3 x minus 24 minus Start Fraction 114 over x plus 3 End Fraction

Answer 1

To create an equivalent form of the rational expression \(-3x^2 - 15x - 18x + 3\), we can first simplify the expression. Let's combine like terms:

\[ -3x^2 - 15x - 18x + 3 = -3x^2 - 33x + 3 \]

Now we can factor this expression. We can factor out a \(-3\):

\[ -3(x^2 + 11x - 1) \]

Next, we will look for ways to factor \(x^2 + 11x - 1\) further or replace it in some equivalent form if possible.

However, the correct factual equivalent would depend on if you're supposed to factor it further or leave it in terms of a fraction.

Let's go through each option to determine if they are equivalent to the original expression:

1. \(-3x - 6\)
2. \(-3x - 114\)
3. This rational expression does not have any equivalent forms.
4. \(-3x - 24 - \frac{114}{x + 3}\)

The rational expression given and the options provided does not provide straightforward forms of equivalence without further context of how they relate to the original expression (as rational expressions can also mean results of some divisions or transformations).

From the options given, none of them seem to be a direct equivalent to \(-3x^2 - 33x + 3\) without applying transformations or simplifications that would require additional information on how the question wants to proceed.

Conclusion: Option "This rational expression does not have any equivalent forms." appears as a valid option unless additional form or context is evaluated with a direct comparison of transformations to other forms presented in the options.