Intro to Factoring (box method)

We know that when we multiply binomials using the area model we will have like terms appear on the diagonal. We notice that these two terms add up to give us the central term in the trinomial. We noticed today that the diagonals in both directions have the same product. We can use these discoveries to help us work backwards.

when we fill in the boxes we multiply. When we are looking for the dimensions on the outside of the box we need to common factor. For example, the bottom row has -6x and +2 we can common factor a -2 from both terms. We place the -2 on the outside of the box, and then can fill in the dimensions at the top of the box, 3x and -1, and then the other dimension missing on the vertical side would be x. The dimensions are in total (3x-1)(x-2). The solutions are below.

We worked hard at the walls in groups to use the area model to expand and also to factor. We are going to keep working on these skills moving forward.