Answer: (x+2) and (x-6) represents the side lengths.
Step-by-step explanation:
The area of the rectangle is [tex]x^{2} -4x -12[/tex] so in this case to find the side lengths we need to factor out the area.
To factor [tex]x^{2} -4x-12[/tex] We need to find two numbers that if we multiply together we will have -12 and if we add those two number we will get -4.
-6 and 2 works out
Because -6 * 2 = -12 and -6 +2 = -4
Now we will rewrite the area as
[tex]x^{2}[/tex] +2x - 6x -12 Group them
([tex]x^{2}[/tex] +2x) (-6x -12) factor them
x (x +2) -6(x+2) factor out x+2
(x+2)(x-6) Done!
