The factorization of
x² + 6x + 8
are
(x + 2)(x + 4)
Notice that across the top there is an x, then a 2,
so the top of the rectangle represents the factor (x + 2)
Notice that down the left side there is an x and below that
is a 4, so the left side of the rectangle represents the
factor (x + 4).
Notice that when we multiply out
(x + 2)(x + 4)
using FOIL, we get
x² + 4x + 2x + 8
The square in the upper left corner has area x², the first term
The rectangle in the lower left has area 4x, the second term
The rectangle in the upper right has area 2x, the third term
The rectangle in the lower right has area 8, the fourth term.
Edwin
