Question
student was asked to solve 4x2−12x=0
by factoring out the GCF.
At what step did the student first make an error?
Given: 4x2−12x=0
Step 1: 4x(x−3)=0
Step 2: 4x=0 and x−3=0
Step 3: x=0 and x=−3
(1 point)
Responses
Step 1
Step 1
Step 2
Step 2
Step 3
by factoring out the GCF.
At what step did the student first make an error?
Given: 4x2−12x=0
Step 1: 4x(x−3)=0
Step 2: 4x=0 and x−3=0
Step 3: x=0 and x=−3
(1 point)
Responses
Step 1
Step 1
Step 2
Step 2
Step 3
Answers
GPT-4o mini
The student made an error in Step 3. The factorization in Step 2 is correct, where they set \( 4x = 0 \) and \( x - 3 = 0 \). However, the solutions derived from Step 3 are incorrect.
From \( 4x = 0 \), the solution is \( x = 0 \), which is correct. But from \( x - 3 = 0 \), the solution is \( x = 3 \), not \( x = -3 \).
So, the answer is **Step 3**.
From \( 4x = 0 \), the solution is \( x = 0 \), which is correct. But from \( x - 3 = 0 \), the solution is \( x = 3 \), not \( x = -3 \).
So, the answer is **Step 3**.