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−24−114x+3 negative 3 x minus 24 minus Start Fraction 114 over x plus 3 End Fraction −3x−6 negative 3 x minus 6 −3x−114 negative 3 x minus 114 This rational expression does not have any equivalent forms. This rational expression does not have any equivalent forms.

Answer 1

To find an equivalent form of the rational expression \(-3x^2 - 15x - 18x + 3\), we first need to combine like terms:

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

Next, we can factor out the common term from the expression. The leading coefficient is \(-3\), which we can factor out:

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

Now, we will check if we can simplify it further by factoring \(x^2 + 11x - 1\), but since it does not factor neatly (using the quadratic formula would be necessary to find the roots), we keep it in the current form.

Now, let’s look at the possible answers given to find the equivalent form.

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

None of the provided options accurately represents the expression we derived: \(-3(x^2 + 11x - 1)\), which suggests that the most appropriate choice based on typical exam structures would be:

This rational expression does not have any equivalent forms.

However, if you'd like to create a single rational expression that neatly combines terms, you could find the common denominator or perform operations to fit it into a form. But from the list provided, it seems no option precisely matches.