Question

Question

Marie divided the expression x2−4x−216x2÷x2−9x2−3x
incorrectly.

First, Marie took the reciprocal of the second term and multiplied: x2−4x−216x2⋅x2−3xx2−9
.

Next, Marie factored each of the terms: (x−7)(x+3)6x2⋅x(x−3)(x+3)(x−3)
.

Finally, Marie canceled terms that were in common and got the answer: x(x−7)6x2
.

Which of the following options explains Marie’s error?

Option #1: Marie factored incorrectly.

Option #2: Marie canceled incorrectly.

Option #3: Marie did not fully simplify the expression.

(1 point)
Option #
shows Marie’s error.

Answer 1

The answer to this question is Option #2: Marie canceled incorrectly.

In the given expression, Marie mistakenly canceled out the common factors (x+3) and (x-3) without multiplying them back with the remaining terms. This caused her to lose those factors in her final answer. Thus, Marie's error lies in her cancellation step.