Review of the Methods of Factoring - Problem 13

Since we know length times width of a rectangle gives us the area, if we start with an area, we should be able to find the length and width. This is the premise for factoring using a box, or geometric representation of a polynomial. The upper left most box must be the ax^2 term, and the bottom right box must be the constant. In order to find what "split" of the bx term to use for the diagonals, you could use a diamond puzzle. You find what two values multiply to the product of a times c and sum to the b value. These two values will be the coefficients on x in the diagonals of the box. Then use greatest common factors of each row and column to find the outsides, or length and width.