I’m thinking most Algebra 2 textbooks include formulas students memorize to factor cubics. Most would include an explanation as to why the formulas work. Many teachers would use those explanations as opportunities to explore patterns if the curriculum is not too densely packed to allow time for that.
On the other hand, college instructors are often dismayed that students arrive without solid understanding of basic Algebra. Too many students have gotten through much of their high school math by memorizing and forgetting a long list of skills, many of which are not found in the CCSS.
Because the logic and patterns behind cubic factoring formulas seems unlikely to stick without a ton of repetition, I replaced the formula lesson with a connection to factoring difference of squares, reinforcing useful skills and avoiding the extraneous.
Idea #1: Factors of simple differences of squares can be found by square rooting, and a factor of a simple binomial cube can found by cube rooting.
Idea #2: Long division, using one factor of a binomial cube, reveals the second (trinomial) factor.
- Difference of squares and binomial cubics
- Long division
- Remainder theorem
Here’s my rough video. Please send me your suggestions for improving this lesson as I am confident others will see things I have missed. There’s no better way to improve, in my opinion, than by listening to others.