Question
The area of the rectangle is 12x3 – 18x2 + 6x. The width is equal to the GCF. What could the dimensions of the rectangle be?
- 6x(2x2 – 3x)
- 3(4x3 – 6x2 + 2x)
- x(12x2 – 18x + 6)
- 6x(2x2 – 3x + 1)
Hint:
In this question, we have to the dimension of the rectangle whose area could be 
, where the GCF is the width. Firstly, we will find the factors of 
and then select the common factors. The product of the common factors will be the GCF. Later, we will take common the GCF from the expression to find the required dimension.
The correct answer is: 6x(2x2 – 3x + 1)
Area of the rectangle =
Factors of 12x3 = 2
23xxx
Factors of -18x2 = (-1)233xx
Factors of 6x = 23x
Common factors = 2, 3, x
GCF = 23x = 6x.
Dimensions of rectangle with area =6x(2x2 – 3x + 1)
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