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−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.

−3x−24−114x+3

Answer 1

Let's simplify the given rational expression:

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

First, combine the like terms:
\[
-3x^2 - (15x + 18x) + 3 = -3x^2 - 33x + 3
\]

Next, let's look to factor out the common factor from the expression. The coefficients of the terms can be factored by -3:

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

Now we can determine if any of the options provided are equivalent to this expression.

However, the options listed do not directly resemble the factored form we simplified to, nor do they provide a clear equivalent expression for \( -3(x^2 + 11x - 1) \).

Given the choices:

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

None of the first two expressions are equivalent to the original rational expression.

The last option may involve a fraction but needs further verification:

- If we consider that \(-3x - 24 - \frac{114}{x + 3}\) suggests combining these terms over a common denominator, it does not simplify to match the form of the original expression.

Based on our analysis, the conclusion is:

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