The area of a rectangular garden is given by the trinomial 2x squared + 2x - 84. What are the possible dimensions of the rectangle?

Begin by factoring out the common factor of 2.

That leaves x^2 + x - 42

Factor this trinomial

Looks like you will be dealing with 6, 7. One is positive and the other is negative. Remember that distance cannot be measured as a negative number.

To find the possible dimensions of the rectangle, we need to factor the given trinomial, 2x^2 + 2x - 84, and then set each factor equal to zero to solve for x.

Step 1: Factor the trinomial
To factor the trinomial, we need to find two binomials whose product is equal to the trinomial. In this case, the factored form would be:
(2x - 6)(x + 14)

Step 2: Set each factor equal to zero and solve for x
Setting the first factor equal to zero:
2x - 6 = 0
Add 6 to both sides:
2x = 6
Divide both sides by 2:
x = 3

Setting the second factor equal to zero:
x + 14 = 0
Subtract 14 from both sides:
x = -14

So, the possible dimensions of the rectangle are:
- Length: x + 14 = -14 + 14 = 0
- Width: 2x - 6 = 2(3) - 6 = 6 - 6 = 0

Therefore, the possible dimensions of the rectangle are length = 0 and width = 0.