Question
QUADRATIC EQUATIONS UNIT TEST:
JEDIDA SOLVED THE QUADRATIC EQUATION X 2 - 96 = 4X BY FACTORING. HER WORK IS SHOWN BELOW. AT WHICH STEP DID JEDIDA FIRST MAKE A MISTAKE, IF AT ALL?
X 2 - 96 = 4 X
STEP 1: X 3 + 4 X - 96 = 0 ADD 4X TO BOTH SIDES.
STEP 2: (X + 12) ( X - 8) = 0 FACTOR
SETP 3: X + 12 = 0 OR X - 8 = 0 USE THE ZERO PRODUCT PROPERTY.
X = -12 OR X = 8
STEP 2: SHE DID NOT FACTOR THE LEFT SIDE OF THE EQUATION CORRECTLY.
STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRAVTING.
SHE DID NOT MAKE ANY MISTAKES.
STEP 3; SHE DID NOT APPY THE ZERO PRODUCT PROPERTY CORRECTLY.
JEDIDA SOLVED THE QUADRATIC EQUATION X 2 - 96 = 4X BY FACTORING. HER WORK IS SHOWN BELOW. AT WHICH STEP DID JEDIDA FIRST MAKE A MISTAKE, IF AT ALL?
X 2 - 96 = 4 X
STEP 1: X 3 + 4 X - 96 = 0 ADD 4X TO BOTH SIDES.
STEP 2: (X + 12) ( X - 8) = 0 FACTOR
SETP 3: X + 12 = 0 OR X - 8 = 0 USE THE ZERO PRODUCT PROPERTY.
X = -12 OR X = 8
STEP 2: SHE DID NOT FACTOR THE LEFT SIDE OF THE EQUATION CORRECTLY.
STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRAVTING.
SHE DID NOT MAKE ANY MISTAKES.
STEP 3; SHE DID NOT APPY THE ZERO PRODUCT PROPERTY CORRECTLY.
Answers
GPT-4o mini
Let's review Jedida's work step by step to determine if she made any mistakes.
Starting with the original equation:
\[
x^2 - 96 = 4x
\]
To rearrange it, we need to move all terms to one side of the equation. We subtract \(4x\) from both sides:
\[
x^2 - 4x - 96 = 0
\]
Now, looking at Jedida's Step 1:
**Jedida's Step 1**: \( x^2 + 4x - 96 = 0 \)
Here she added \(4x\) instead of subtracting it, which is incorrect. This is where her first mistake occurs.
Next:
**Jedida's Step 2**: She factored incorrectly. The correct factorization of \(x^2 - 4x - 96\) should yield different factors. However, the error in Step 1 means that the factors she arrives at in Step 2 are already based on an incorrect equation.
Finally,
**Jedida's Step 3**: While she uses the zero product property correctly to find the roots, her results are based on incorrect factors.
Based on this breakdown, the first mistake Jedida made was in **Step 1** where she added \(4x\) to both sides instead of subtracting it. Therefore, the correct answer is:
**STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRACTING.**
Starting with the original equation:
\[
x^2 - 96 = 4x
\]
To rearrange it, we need to move all terms to one side of the equation. We subtract \(4x\) from both sides:
\[
x^2 - 4x - 96 = 0
\]
Now, looking at Jedida's Step 1:
**Jedida's Step 1**: \( x^2 + 4x - 96 = 0 \)
Here she added \(4x\) instead of subtracting it, which is incorrect. This is where her first mistake occurs.
Next:
**Jedida's Step 2**: She factored incorrectly. The correct factorization of \(x^2 - 4x - 96\) should yield different factors. However, the error in Step 1 means that the factors she arrives at in Step 2 are already based on an incorrect equation.
Finally,
**Jedida's Step 3**: While she uses the zero product property correctly to find the roots, her results are based on incorrect factors.
Based on this breakdown, the first mistake Jedida made was in **Step 1** where she added \(4x\) to both sides instead of subtracting it. Therefore, the correct answer is:
**STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRACTING.**