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

−3x−114
negative 3 x minus 114

−3x−6
negative 3 x minus 6

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

−3x−24−114x+3
only use these answers

Answer 1

To simplify the expression \(-3x^2 - 15x - 18x + 3\) first combine like terms:

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

Next, we can factor out \(-3\) from the expression:

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

Since the question asks for equivalent forms of the rational expression, we see the option \(-3x - 6\).

Let's evaluate the provided answer options:

1. −3x−114: This does not simplify from \(-3(x^2 + 11x - 1)\).
2. −3x−6: This is not an equivalent simplified version of the original expression.
3. This rational expression does not have any equivalent forms: This could be considered correct as the previous factors are not equivalent forms of the provided expression.
4. −3x−24−114x+3: This expression does not correspond to any simplification of the provided numerator.

Among the available options, “This rational expression does not have any equivalent forms” is the most fitting response, as none of the other options accurately reflect a simplification of the original expression.