7. Jason solved the quadratic equation x2−4x−12=0

Question

by factoring. His work is shown below.

Step 1: x2−4x−12=0
Step 2: (x-6)(x+2)=0

Step 3: x - 6 = 0, x + 2 = 0

Step 4: x = 6 or x = 2

Step 5: {6,2}

Jason plugged his solutions into the original equation, and found that they did not work. In which step did he first make a mistake?

(1 point)
Responses

Step 1
Step 1

Step 2
Step 2

Step 3
Step 3

Step 4

Answer 1

Jason made his first mistake in Step 2.

The correct factoring of the quadratic equation \(x^2 - 4x - 12 = 0\) is \((x - 6)(x + 2) = 0\). However, the correct solutions from those factors should be \(x - 6 = 0\) leading to \(x = 6\) and \(x + 2 = 0\) leading to \(x = -2\), not \(x = 2\).

So, the error occurs at Step 2 where he incorrectly stated the factored form's solutions. Therefore, the first mistake is in Step 2.