Answer:
2x -3
Explanation:
Given a rectangle with area 2x²+x-6 and one dimension x+2, you want the other dimension.
Area
The area of a rectangle is the product of its length and width. Given the area and the width, we can solve for the length:
A = LW
A/W = L
So, the missing dimension is the quotient of (2x²+x-6) and (x+2). In the attached, we find that quotient by synthetic division.
The missing dimension is 2x -3.
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Additional comment
You can also use any of several methods to factor the area expression. We recognize that numbers of interest will be factors of (2)(-6) that total +1. Those would be -3 and +4. Then we can write ...
A = 2x² +x -6 = (2x -3)(2x +4)/2 = (2x -3)(x +2)
We recognize the factor (x+2) as the given dimension, so the missing dimension is (2x -3).