Factoring

We are working on factoring algebraic expressions.  Today we visualized this by makingg rectangles out of algebra tiles.

The area inside the rectangle is the trinomial x^2+7x+12 and the factors are the length and width of the rectangle (x+3)(x+4).  This is the only combination of length and width that work for this polynomial.  We also noticed that there is a pattern.  3+4=7 (the middle coefficient of the polynomial) and 3×4=12, the constant term.