Area Model for Factoring and Multiplying

We looked at polynomials today in grade 10, we made rectangles out of the algebra tiles that represent a given polynomial.  This example is x^2+5x+6.  We can see the dimensions of our rectangle are (x+3) and (x+2).

We looked at how the numbers in the equation are related.  To be able to make a rectangle we need specific values for the constant.

We know that the 8x can be arranged in a few ways, and each way leads to a different constant.

We can do the same if the constant is given but the number of x is unknown.  In this case, if the constant is 10, we look for the ways we can arrange 10 tiles in a rectangle.  We can do it as 1×10 or 2×5 so that will give us options of 11 or 7 x tiles to complete the rectangle.