Question
Jedida solved the quadratic equation x2−96=4x
by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?
(1 point)
Responses
Step 1; she added 4x to both sides instead of subtracting.
Step 1; she added 4x to both sides instead of subtracting.
She did not make any mistakes.
She did not make any mistakes.
Step 3; she did not apply the Zero Product Property correctly.
by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?
(1 point)
Responses
Step 1; she added 4x to both sides instead of subtracting.
Step 1; she added 4x to both sides instead of subtracting.
She did not make any mistakes.
She did not make any mistakes.
Step 3; she did not apply the Zero Product Property correctly.
Answers
Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 - 96 = 4x \) by factoring, we first rearrange the equation:
1. Subtract \( 4x \) from both sides:
\[
x^2 - 4x - 96 = 0
\]
Now let's analyze Jedida's steps:
If she keeps the equation correctly, we can move on to factor it, which might look like this:
2. Factor the left side to find:
\[
(x - 12)(x + 8) = 0
\]
3. Apply the Zero Product Property:
\[
x - 12 = 0 \quad \text{or} \quad x + 8 = 0
\]
From the above analysis, Jedida's initial manipulation to rearrange and factor the equation is correct. However, if there was an error at any stage, it would typically be an issue in her factoring or application of the Zero Product Property.
Since we don't have her specific steps detailed, but just the options presented, the answer can only be inferred based on common mistakes.
If she incorrectly performed the operations or factoring at any step, this will lead us to the choices given.
1. If she added instead of subtracting in the first step, that could definitely be a mistake.
2. The comment about the Zero Product Property suggests that if her factors were incorrect, she may have also misapplied the property.
However, since the original equation was changed correctly to \( x^2 - 4x - 96 = 0 \), the likely first mistake can be traced back to an erroneous manipulation in the addition/subtraction.
If we strictly follow the logic of first steps leading to potential mistakes, the most likely answer is:
**Step 1; she added 4x to both sides instead of subtracting.**
1. Subtract \( 4x \) from both sides:
\[
x^2 - 4x - 96 = 0
\]
Now let's analyze Jedida's steps:
If she keeps the equation correctly, we can move on to factor it, which might look like this:
2. Factor the left side to find:
\[
(x - 12)(x + 8) = 0
\]
3. Apply the Zero Product Property:
\[
x - 12 = 0 \quad \text{or} \quad x + 8 = 0
\]
From the above analysis, Jedida's initial manipulation to rearrange and factor the equation is correct. However, if there was an error at any stage, it would typically be an issue in her factoring or application of the Zero Product Property.
Since we don't have her specific steps detailed, but just the options presented, the answer can only be inferred based on common mistakes.
If she incorrectly performed the operations or factoring at any step, this will lead us to the choices given.
1. If she added instead of subtracting in the first step, that could definitely be a mistake.
2. The comment about the Zero Product Property suggests that if her factors were incorrect, she may have also misapplied the property.
However, since the original equation was changed correctly to \( x^2 - 4x - 96 = 0 \), the likely first mistake can be traced back to an erroneous manipulation in the addition/subtraction.
If we strictly follow the logic of first steps leading to potential mistakes, the most likely answer is:
**Step 1; she added 4x to both sides instead of subtracting.**