It is possible to construct geometric models for factorizati

It is possible to construct geometric models for factorizations so that you can see the factoring. This idea is developed in Exercises 95-96. Consider the following figure. Write a trinomial that expresses the sum of the areas of the six rectangular pieces shown in figure (a). Express the area of the large rectangle in figure (b) as the product of two binomials.

Solution

a) Area of areas in figure a) x^2 + x*1+x*1+x*1 +1*1+1*1

= x^2 + 3x + 2

b) In figure b)

length = x+2

width = x+1

Area = (x+1)(x+2)