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)
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Hello there! :)

First choice, (x + 2) and (x - 6).

Step-by-step explanation:

To solve for the dimensions, recall that the formula for the volume of a rectangle is:

A = l × w

Simply factor x² -4 - 12. Find two numbers that add up to -4 and multiply into -12.

2, -6 satisfy these conditions. Use these numbers to write this equation in factored form:

(x + 2) (x - 6). Thus, the first option is the correct answer.

(x-6) (x+2)

Step-by-step explanation:

x^2 - 4x – 12

Factor

What two numbers multiply to -12 and add to -4

-6*2 = -12

-6+2 = -4

(x-6) (x+2)

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

1 1/4 hours

step-by-step explanation:

2/4 + 2/4 + 1/4 = 5/4 or 1 1/4