I've been able to consistently teach my Algebra 1 students how to factor polynomials with 2, 3, or 4 terms using a 4-day plan. On the first day, I focus on trinomials, but introduce them to the "box", "generic rectangle," or "area model" to represent the terms of a trinomial.
I emphasize the fact that the "diagonal products," much like "cross-products", are always equal. (To see this, please hover over thumbnail 2, and you'll see that both diagonals have the same product, in this case, - 90x^2).
I also tell them always to put the two most "unlike" terms (in this case, 6x^2 and -15) in opposite corners, which facilitates the process.
On the second day, I throw in binomials, and have the students add in a "middle term" or "+0x" term if they need.
On the third day, I have them factor out a GCF first, and then factor the remaining polynomials.
On the fourth and last day, I throw in what many teachers might call "factoring by grouping," which is basically used for factoring polynomials with 4 terms. Again, I have them put the two most unlike terms in opposite corners, and the other two terms in the remaining corners. After they factor that, I have them see if they can continue to break down any factors, such as the difference of squares.
This is the worksheet for the third day.
The file includes spiral review problems.
For this worksheet, I expect students to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.