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

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

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

C. −3x−114
negative 3 x minus 114

D.−3x−6
negative 3 x minus 6

Answer 1

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

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

2. Factor out the common term: \[ = -3(x^2 + 11x - 1) \]

Now, let's look at the options provided:

A. This rational expression does not have any equivalent forms.
This is incorrect, as there are equivalent forms for any rational expression.

B. \(-3x - 24 - \frac{114}{x + 3}\)
This looks complicated and does not resemble our expression.

C. \(-3x - 114\)
This seems incorrect, as simplifying does not produce this result.

D. \(-3x - 6\)
This also does not match our simplified version.

None of the options presented seem to correctly represent an equivalent form of the original expression. If I were to choose the correct equivalent form, it’s not among the options given.

Please verify the options or assumptions for errors, as the presented options do not yield correct equivalents for the original expression.

Answer 2

Pick the most correct option

Answer 3

Based on the options provided and the fact that none of them perfectly match the simplified version of \(-3x^2 - 33x + 3\) or its factored form, we need to analyze which option might be the most reasonable fit.

Given the provided choices:

• A: Incorrect, as equivalent forms definitely exist.
• B: This is not simplified correctly or equivalent to the original.
• C: This form is incorrect, as it mismatches the expression.
• D: This form is also not equivalent to the original expression.

None of the options are correct equivalents; however, if we are to select the closest** option considering simplification and form errors, none represent an equivalent form.

In conclusion, given that all options are incorrect, the logical response remains that the most appropriate action would be to verify the correctness of the options themselves in your context, as the expression does have equivalent forms, which are not correctly provided.

If forced to choose one, I cannot justifiably select any because they all contain inaccuracies concerning the original expression. Would you like any further assistance in handling the question or verifying another aspect?