Factorising by Grouping SB

The Problem

As with most of the Maths that I think about I got pretty obsessed with Factorising by Grouping after doing a question on Brilliant.org. (I will not spend too much time here talking about how much I love Brilliant.org but I absolutely absolutely love Brilliant.org and think that anyone that is interested in Maths and Problem Solving would love scrolling through its hallowed courses)

I was also in the process of discussing the factor theorem with my year 11 students and was repeatedly asked “Do I just use trial and error to find a factor”. As well as this technique works it doesn’t feel all that satisfying and certainly there is more fun maths to be found here if we look around.

The Fun Maths

When putting together exercises to try and practise this skill I started with using factorising by grouping to factorise quadratics – something that the students were confident in and had seen before.

As the worksheet progressed the questions slowly increase in difficulty, with the scaffolding being taken away in steps.

Eventually moving on to some all together more tricky cubics that require a splitting of the middle terms. This is a technique that is often used to factorise quadratics where the coefficient of the x squared term >1 but I had never seen it used to factor cubics.

Its these questions that I think were particularly fun to play around with as it is not immediately obvious how to split our terms nicely. I would encourage you to try to complete these questions as well as the rest of the questions on the sheet.

Post Credits

As we continued to try this out with different cubics it felt like we were once again using trial and improvement to work out how to split these trickier cubics up. It didn’t feel like a fruitless exercise as working out why your choices weren’t working and trying to choose better options feels like it has great benefit in become more fluent in your algebraic manipulation and also was just a fun way to practise lots of smaller expanding and factoring skills. It is always fun to practise these skills using deeper problems!

I spent a long time trying to come up with a clear method for factoring cubics by grouping when then grouping isn’t immediately obvious and I am still struggling! If you come up with anything please let me know at chelekmaths@gmail.com – I am excited to keep learning!

This is a link to the worksheet – click to download. You can also find it in the Slow Build section of the website as well as on our resources page.

NJK