This week we learned how to factor polynomials using area models. I really enjoy using area models, as I am a visual learner this is super helpful at breaking down the question so that it is easier to factor in the end. when we first learned this, I was confused about what to fill in the box with and what to use from the box as the `result of factoring. once I learned how to do it I got better at using the area model.

when solving a polynomial using an area model you should…

Let’s try that first expansion with an area model:

(3x + 4)(2x – 5)

We’ve got 2 terms in each factor, so we set up a 2×2 area model like this…

We’re using the same principle of deconstruction that we use with multiplying large numbers, breaking up the polynomials into their terms. Next, we fill in the model using multiplication…

…then add the products together, combining like terms…

something that I struggled with in the beginning while working with the area model was not knowing what number to place on the inside, and not knowing/ understanding what to multiply to find the missing numbers in the square. with some extra help and more focus, I was able to realize that the numbers on the inside were the product of the multiplication within the outside of the box. For example, if you had a binomial box (meaning split into two) and the first box had x squared and the other box had 6x that would mean on the outside would be (x) on the right-hand side, and on the top above the first box would also be (x), and beside the (x) would be a (6). because x times x equal x squared and x multiplied by 6 is equal to 6x. Once I had gotten the hang of it it was super simple and very helpful to use while solving/simplifying.

I have chosen this topic for this week because area models are super important to have, especially if you are a visual learner like myself they are a handy tool to understand and use while solving polynomials, trinomials, and more. You can use area models to help you multiply large numbers.  Show the problem as the area of a rectangle, and then break that rectangle into smaller chunks for easier solving.

Citation:

Sorensen, E. (2021, November 23). How to expand polynomials using area models: The anti-FOIL method. Emergent Education Portland Tutoring & Test Prep. https://emergenttutoring.com/blog/how-to-expand-polynomials-using-area-models-the-anti-foil-method/