Question

A student performed the following steps to find the solution to the equation x²-2x-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. in Step 1
B. in Step 2
C. The student did not make any mistakes, the solution is correct
D. in Step 3

Answer 1

The error was made at Step 1 in the factorization process. The correct factors should be (x-4)(x+2), leading to solutions x=4 and x=-2.

Step-by-step explanation:

The student made an error in Step 1 of solving the equation x²-2x-8=0. The correct factorization of the quadratic polynomial is (x-4)(x+2), not (x-4)(x-2) as the student performed.

When factored correctly, the equation becomes (x-4)(x+2)=0, which leads to Step 2: solving the individual factors for x: x-4=0 results in x=4, and x+2=0 results in x=-2.