Question

a rectangle with an area of $x^2 - 4x - 12$ square units is represented by the model.
what side lengths should be used to model the rectangle?
$\circ$ $(x + 2)$ and $(x - 6)$
$\circ$ $(x + 6)$ and $(x - 2)$
$\circ$ $(x + 2)$ and $(x - 10)$
$\circ$ $(x + 10)$ and $(x - 2)$

Explanation:

Step1: Factor the quadratic expression

We need to factor \(x^2 - 4x - 12\). We look for two numbers that multiply to \(-12\) and add up to \(-4\). The numbers are \(-6\) and \(+2\) because \((-6)\times(2)=-12\) and \(-6 + 2=-4\). So, \(x^2-4x - 12=(x + 2)(x - 6)\).

Step2: Match with the options

Now we check the options. The factored form \((x + 2)(x - 6)\) matches the first option.

Answer:

\((x + 2)\) and \((x - 6)\) (the first option among the given choices)