Question

the area of a rectangle is 30 + 12x. list three possibilities for the length and width of the rectangle. length width

Explanation:

Step1: Factor out 1

The area is \(30 + 12x=1\times(30 + 12x)\), so length could be \(1\), width \(30 + 12x\).

Step2: Factor out 2

Factor out 2: \(30 + 12x = 2\times(15 + 6x)\), so length \(2\), width \(15 + 6x\).

Step3: Factor out 3

Factor out 3: \(30 + 12x=3\times(10 + 4x)\), so length \(3\), width \(10 + 4x\).

Answer:

Length	Width
2	\(15 + 6x\)
3	\(10 + 4x\)

(Other valid factorizations like factoring out 6 (\(6\times(5 + 2x)\)) or using different factoring approaches are also acceptable, these are three possible ones.)