Hyung-eun is solving the quadratic equation x2−4x−12=0 by grouping. Her work is shown below. At which step does Hyung-eun first make an error? x2−4x−12=0 Step1: x2+(−6x)+2x−12=0 Step 2: (x2+(−6x))+(2x−12)=0 Step 3: x(x+(−6))+2(x−6)=0 x(x−6)+2(x−6)=0 Step 4: (x+6)(x−2)=0 Step 5: x+6=0 or x−2=0 x=−6 or x=2
Step 4
Step 3
Step 2
Step 1
In order to determine where Hyung-eun first makes an error, let's go through the steps and check for any mistakes.
Step 1: x2 + (−6x) + 2x − 12 = 0
In this step, Hyung-eun correctly rewrites -4x as -6x + 2x to create two sets of terms that can be grouped together.
Step 2: (x2 + (−6x)) + (2x − 12) = 0
Here, Hyung-eun correctly groups the terms by adding the terms in the parentheses.
Step 3: x(x + (−6)) + 2(x − 6) = 0
In this step, Hyung-eun wants to factor out the common factors of the two sets of parentheses. However, there is an error. The factorization should be x(x - 6) + 2(x - 6), not x(x + (-6)) + 2(x - 6).
Step 4: (x + 6)(x - 2) = 0
In this step, Hyung-eun correctly applies the distributive property to multiply the factored form.
Step 5: x + 6 = 0 or x - 2 = 0
Here, Hyung-eun correctly sets each factor equal to zero and solves for x.
Therefore, the error occurs in Step 3. The correct factorization should be x(x - 6) + 2(x - 6), not x(x + (-6)) + 2(x - 6).