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?

a. (x+2) and (x−6)
b. (x+6) and (x−2)
c. (x+2) and (x−10)
d. (x+10) and (x−2)

Answer 1

To find the side lengths for a rectangle with an area of x^2 - 4x - 12, we factor the expression to get (x + 2) and (x - 6), which are the required side lengths.

Step-by-step explanation:

We need to determine the side lengths that would model a rectangle with an area of x2 - 4x - 12 square units. To find the side lengths, we can factor the quadratic expression into a product of two binomials.

Factoring the quadratic expression, we look for two numbers that multiply to -12 and add up to -4. These numbers are +2 and -6. So we factor the expression as follows:

• (x + 2)(x - 6) = x2 - 4x - 12

Thus, the side lengths that should be used to model the rectangle are (x + 2) and (x - 6).