Question

describe and correct the error a student made in factoring
$x^2 + 2x - 3 = 5$
$(x - 1)(x + 3) = 5$
$x - 1 = 5$ or $x + 3 = 5$
$x = 6$ or $x = 2$
the student did not take the square root of both sides first
find the correct solution(s)
$x = $
(simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Rearrange to standard form

$x^2 + 2x - 3 - 5 = 0$
$x^2 + 2x - 8 = 0$

Step2: Factor the quadratic

$(x + 4)(x - 2) = 0$

Step3: Apply zero product rule

$x + 4 = 0$ or $x - 2 = 0$

Step4: Solve for x

$x = -4$ or $x = 2$

Error Description:

The student incorrectly applied the zero product rule to an equation not set equal to 0. They factored the left side while the right side was 5, which is invalid for this method. The correct first step is to rearrange the equation so one side is 0 before factoring.

Answer:

$x = -4, 2$