Question

The area of a rectangle is given as A = 3x² + 5x – 2.
Find the factors of the expression. What may be
the length and the breadth of the rectangle?​

Answer 1

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The expression factors as (3x-1)(x+2)

However, there are lots of other ways to divide things up. For example, if x=3, the area is 8*5 = 40, but those are not the only two ways to get two numbers which multiply to 40.

Answer 2

$a = {3x}^{2} + 6x - x - 2 = \\ 3x(x + 2) - 1(x + 2) = \\ (3x - 1)(x + 2)$