A student was asked to solve 2x2−10x=0 by factoring out the GCF.

Question

At what step did the student first make an error?

Given: 2x2−10x=0
Step 1: 2x(x−10)=0
Step 2: 2x=0 and x−10=0
Step 3: x=0 and x=10(1 point)
Responses

Step 1
Step 1

Step 2
Step 2

Step 3

Answer 1

The student made an error in Step 1.

The original equation is \( 2x^2 - 10x = 0 \).

When factoring out the greatest common factor (GCF), it should be:

\[ 2x(x - 5) = 0 \]

The student incorrectly factored it as \( 2x(x - 10) = 0 \).

As a result, the correct factored form is not achieved, and thus Step 1 is where the error first occurred.