Question

Shau-uen solved the equation x² + 4x - 5 = 0. Her work is shown in the steps below:

Step 1: x² + 4x - 5 = 0 Step 2: x² + 5x - x - 5 = 0 Step 3: x (x + 5) - 1 (x + 5) = 0 Step 4: (x - 1) (x + 5) = 0 In which step did Shau-uen make her first error?
a) Step 1
b) Step 2
c) Step 3
d) Step 4

Answer 1

Shau-uen made her first error in Step 3 by factoring out a common binomial incorrectly.

Step-by-step explanation:

Shau-uen made her first error in Step 3.

In Step 3, Shau-uen tried to factor out a common binomial, but she made an error in the signs. Instead of subtracting (x - 1), she mistakenly subtracted (x + 1) from (x + 5). The correct factorization should be (x - 1)(x + 5) = 0.

Therefore, the correct answer is c) Step 3.