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

Answer 1

The student made a mistake in Step 1 (option A) by incorrectly factoring the quadratic equation x² - 2x - 8. The correct factors should be (x - 4)(x + 2), leading to solutions x = 4 and x = -2.

Step-by-step explanation:

The student's error occurs in Step 1 of solving the equation x² - 2x - 8 = 0.

The polynomial they factored into (x - 4) and (x + 2) is incorrect.

Proper factoring of the quadratic equation x² - 2x - 8 would result in (x - 4)(x + 2).

After factoring correctly, the solution is found by setting each factor equal to zero, which gives the roots x = 4 and x = -2.

To find the correct factors of a quadratic equation, you can use the quadratic formula, look for a perfect square, or try to factor by recognizing patterns or by trial and error. The correct option that points out where the student went wrong is option B, in Step 1.