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)

Question

Responses

This rational expression does not have any equivalent forms.
This rational expression does not have any equivalent forms.

−3x−24−114x+3
negative 3 x minus 24 minus Start Fraction 114 over x plus 3 End Fraction

−3x−114
negative 3 x minus 114

−3x−6
negative 3 x minus 6

Answer 1

To find an equivalent form of the rational expression \(-3x^2 - 15x - 18x + 3\), we first simplify it.

Combine like terms: \[ -3x^2 - 15x - 18x + 3 = -3x^2 - 33x + 3 \]

Next, we can factor out the common factor from the expression: \[ -3(x^2 + 11x - 1) \]

Now let's look at the options provided to see which one matches an equivalent form of this expression.

1. This rational expression does not have any equivalent forms.

   This is incorrect; every rational expression typically has equivalent forms based on factoring and simplification.

2. \(-3x - 24 - \frac{114}{x + 3}\)

   To verify this option, we would need to connect it back to the expression we simplified, but it appears quite different, and it does not seem to simplify to our expression.

3. \(-3x - 114\)

   This is not equivalent to our expression since it does not include the \(x^2\) term or represent the original polynomial correctly.

4. \(-3x - 6\)

   This expression also lacks the correct \(x^2\) component and doesn't represent the original expression correctly.

None of the provided options correctly represent an equivalent form of the original rational expression after simplification. Thus, the most accurate response would be that none of the options provided are equivalent forms of the original rational expression.

Please note that if the expression to be simplified was incomplete or there was a typographical error, we could look at it again. But as it stands, none of the options match.