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
O A. in Step 1
B. The student did not make any mistakes, the solution is correct
C. in Step 2
D. in Step 3

Answer 1

A. Step 1

Explanation:

Hello!

Let's solve the quadratic ourselves and see what went wrong with the student's steps.

Step 1: Factor the expression

Over here, I'm going to rewrite -2x as the expression 2x - 4x so it would be easier to factor. Basically what I'm finding is "What two numbers multiply to -8, and add up to -2?"

I find the solution to that question: 2 and -4

• x² - 2x - 8 = 0
• x² + 2x - 4x - 8 = 0
• x(x + 2) - 4(x + 2) = 0
• (x-4)(x+2) = 0

Step 2: Find the roots

Set the factors equal to 0.

1. x - 4 = 0, x = 4
2. x + 2 = 0, x = -2

Final Thoughts

We can see that the student made a mistake in step 1, as he did not factor the expression correctly.

The student got the factored expression as (x - 4)(x - 2) which multiplies out to x² - 6x + 8, which is not the same expression given.

Our solution, (x - 4)(x + 2) gives us x² - 2x - 8, which is correct.