Exercise 2 Page 89

We can follow the steps given in Exploration 1 to factor a polynomial by using algebra tiles.

1. Arrange the algebra tiles that model the product in a rectangular array.
2. Use additional algebra tiles to model the dimensions of the rectangle.
3. Write the polynomial in factored form using the dimensions of the rectangular array.

For example, consider that we want to factor the product x^2+4x+3. Therefore, we should first represent this expression using algebra tiles. Then, we need to arrange them in a rectangular array.

Now, using additional algebra tiles we model the dimensions of the rectangular array obtained in the previous step.

Since the area of a rectangle is obtained as the product of its dimensions, we can factor the original expression as the product of the expressions representing the dimensions of the rectangular array. x^2+4x+3_(Area) = (4+1)_(Width) (4+3)_(length)