Question

A rectangle with an area of x2 – 4x – 12 square units is represented by the model. What side lengths should be used to model the rectangle? (x + 2) and (x – 6) (x + 6) and (x – 2) (x + 2) and (x – 10) (x + 10) and (x – 2)

Answer 1

Answer: The correct answer is A (x+2)(x-6) on Edg 2020;)

Answer 2

Answer: (x+2) and (x-6) represents the side lengths.

Explanation:

The area of the rectangle is
`x^(2) -4x -12` so in this case to find the side lengths we need to factor out the area.

To factor
`x^(2) -4x-12` 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

`x^(2)` +2x - 6x -12 Group them

(
`x^(2)` +2x) (-6x -12) factor them

x (x +2) -6(x+2) factor out x+2

(x+2)(x-6) Done!