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 polynomial factoring

For the quadratic polynomial \(x^{2}-2x - 8\), we use the formula \(x^{2}+bx + c=(x + m)(x + n)\) where \(m + n=b\) and \(mn=c\). Here \(b=-2\) and \(c = - 8\). We need two numbers \(m\) and \(n\) such that \(m + n=-2\) and \(mn=-8\). The numbers are \(m = 2\) and \(n=-4\) since \(2+( - 4)=-2\) and \(2\times(-4)=-8\). So the correct factoring is \((x - 4)(x+2)\), not \((x - 4)(x - 2)\) as in the student's step 1.

Step2: Analyze subsequent steps

Since step 1 is wrong, steps 2 and 3 which are based on the wrong - factored form are also wrong, but the first error is in step 1.

Answer:

B. Step 1