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)%0D%0AResponses%0D%0A%0D%0AThis rational expression does not have any equivalent forms.%0D%0AThis rational expression does not have any equivalent forms.%0D%0A%0D%0A−3x−6%0D%0Anegative 3 x minus 6%0D%0A%0D%0A−3x−114%0D%0Anegative 3 x minus 114%0D%0A%0D%0A−3x−24−114x+3

Answer 1

To simplify the expression \(-3x^2 - 15x - 18x + 3\), let's start by combining like terms.

1. Combine the \(x\) terms: \[ -15x - 18x = -33x \]

2. So the expression becomes: \[ -3x^2 - 33x + 3 \]

Now, we can factor out the greatest common factor from the expression. The greatest common factor here is \(-3\): \[ -3(x^2 + 11x - 1) \]

Next, let's see if we can factor \(x^2 + 11x - 1\), but that does not directly lead to simpler expressions in the options provided.

To determine if any of the options represent an equivalent form, let's analyze the answers given:

1. \(-3x - 6\): This cannot be equivalent since it is a linear expression and we started with a quadratic.

2. \(-3x - 114\): Again, this is linear and does not represent a quadratic form.

3. \(-3x - 24 - \frac{114}{x + 3}\): This expression looks complex but has fractions involved, which generally indicates that it's not equivalent to the original polynomial expression.

Given this, it seems that none of the simplified forms directly correspond to the equivalent rational expression.

Thus, the final answer would be that the original expression does not have any of the suggested equivalent forms, and the choice is: This rational expression does not have any equivalent forms.