Step-by-step explanation:
the area is
length × width
(3x - 2) × width = 9x² - 4
to find width we could do a real polynomial division or simply recognize the fact that
(a + b)(a - b) = a² - b²
and we see that in our area calculation we are missing the (a + b) factor.
so, width = (3x + 2)
but if you want the division :
9x² - 4 : 3x - 2 = 3x + 2
- 9x² - 6x
-----------------
0 6x - 4
- 6x - 4
----------------------
0 0
again, width = (3x + 2)
