Question

question 8 of 10
a student performed the following steps to find the solution to the equation $x^{2}-2x - 8=0$. where did the student go wrong?
step 1. factor the polynomial into (x - 4) and (x - 2)
step 2. x - 4 = 0 and x - 2 = 0
step 3. x = 4 and x = 2
a. step 3
b. step 1
c. step 2
d. the student did not make any mistakes. the solution is correct.

Explanation:

Step1: Check the factoring

The correct factoring of \(x^{2}-2x - 8=0\) should be \((x - 4)(x+2)=0\) since \((x - 4)(x + 2)=x^{2}+2x-4x - 8=x^{2}-2x - 8\), not \((x - 4)(x - 2)\) as in step 1.

Step2: Analyze other steps

Steps 2 and 3 are based on the incorrect factoring in step 1. But the error - origin is in step 1.

Answer:

B. Step 1