percy solved the equation $x^{2}+7x + 12 = 12$. his work is shown below. is percy correct? explain.\n1. $(x…

Answer:

Percy is not correct.

Explanation:

Step1: Rewrite the original equation

The original equation is $x^{2}+7x + 12=12$. Subtract 12 from both sides to get $x^{2}+7x=0$.

Step2: Factor the correct equation

Factor out an $x$ from $x^{2}+7x$, we have $x(x + 7)=0$.

Step3: Apply zero - product property

According to the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$. So $x=0$ or $x+7=0$, which gives $x = 0$ or $x=-7$.

Step4: Analyze Percy's error

Percy wrongly applied the zero - product property. The zero - product property states that if $ab = 0$, then $a = 0$ or $b = 0$. But in his work, $(x + 3)(x + 4)=12$, since 12 is not 0, we cannot set $x + 3=12$ or $x + 4=12$.