Question

Meghan simplified the expression x2−5x−24x2−3x incorrectly.

First, she factored each of the terms: (x−8)(x+3)x(x−3).

Next, she canceled the binomials in common: (x−8)x.

Finally, she canceled any of the x’s that were in common and got the answer (x−8)x.

(1 point)
Responses

Meghan factored incorrectly.
Meghan factored incorrectly.

Meghan canceled the binomials incorrectly.
Meghan canceled the binomials incorrectly.

Meghan canceled the x’s incorrectly.
Meghan canceled the x ’s incorrectly.

Meghan did not solve the problem incorrectly. All steps were completed correctly.

Answer 1

To analyze Meghan's work, let's look at her steps more closely:

1. **Factoring the Expression**: The original expression is \( \frac{x^2 - 5x - 24}{x^2 - 3x} \).

- The numerator \( x^2 - 5x - 24 \) factors to \( (x - 8)(x + 3) \).
- The denominator \( x^2 - 3x \) can be factored as \( x(x - 3) \).

So the correct factorization should be:
\[
\frac{(x - 8)(x + 3)}{x(x - 3)}
\]
Therefore, Meghan's factorization is correct at this stage.

2. **Canceling Binomials**: Meghan canceled the binomials incorrectly. The factors do not have common factors to cancel.

The factored form should remain as:
\[
\frac{(x - 8)(x + 3)}{x(x - 3)}
\]
There are no common factors to simplify here.

3. **Canceling the x's**: Since she made an error in the binomial cancellation, it doesn't reach the point where canceling 'x' can be assessed correctly. Thus, this part of her simplification is incorrect based on her prior mistake.

### Conclusion:
The correct answer is:
- **Meghan canceled the binomials incorrectly.**