Question

homework 9.2
due
feb 5-11:45 pm late
part 1 of 2
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 $x = 2$
describe the error. choose the correct answer below
a. the student did not get 0 on one side of the equation
b. the student did not solve the two equations for x correctly
c. the student did not factor correctly
d. the student did not take the square root of both sides first
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Explanation:

Step1: Recall zero product rule

The zero product property states that if $ab=0$, then $a=0$ or $b=0$. It only applies when the product equals 0, not a non-zero number like 5.

Step2: Analyze student's work

The student factored $x^2+2x-3$ to $(x-1)(x+3)$, then set each factor equal to 5. This violates the zero product rule because the right-hand side was not first rewritten to 0.

Step3: Correct the process

First, rearrange the original equation to get 0 on one side:
$$x^2 + 2x - 3 - 5 = 0$$
$$x^2 + 2x - 8 = 0$$
Factor the quadratic:
$$(x+4)(x-2)=0$$
Apply zero product rule:
$x+4=0$ or $x-2=0$, so $x=-4$ or $x=2$

Answer:

A. The student did not get 0 on one side of the equation