Question

describe and correct the error a student made in factoring

the students work is shown below (with a red x indicating an error):

$x^2 + 2x - 3 = 5$
$(x - 1)(x + 3) = 5$
$x - 1 = 5$ or $x + 3 = 5$
$x = 6$ or $x = 2$

multiple - choice options:
a. the student did not factor correctly
b. the student did not solve the two equations for x correctly
c. the student did not get 0 on one side of the equation.
d. the student did not take the square root of both sides first.

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Explanation:

Step1: Identify error source

To use factoring for solving a quadratic equation, the equation must first be rearranged so that one side equals 0. The student skipped this step.

Step2: Correct initial equation

Subtract 5 from both sides to set the equation to 0:
$x^2 + 2x - 3 - 5 = 0$
$x^2 + 2x - 8 = 0$

Step3: Factor the quadratic

Factor the corrected quadratic expression:
$(x + 4)(x - 2) = 0$

Step4: Solve for x

Set each factor equal to 0 and solve:
$x + 4 = 0 \implies x = -4$
$x - 2 = 0 \implies x = 2$

Answer:

C. The student did not get 0 on one side of the equation.
Correct solutions: $x = -4$ or $x = 2$