Factorising – the Opposite of Expanding

For many learners in S3, this is the next big step in making sense of algebra

Next to expanding brackets, factorising is one of the most important skills for making sense of algebraic expressions.

It often appears just as learners are starting to feel more comfortable and, in many ways, it becomes even more important.

The results of this crucial skill are not appreciated for some time yet, but familiarity and comfort with factorising will reap benefits and eliminate future headaches.

This is often the point where learners realise algebra isn’t just about working things out. Instead, it’s about recognising structure.

Why factorising is important

Factorising reveals the solution for an expression when it becomes an equation. At this stage, learners move from simply calculating answers to understanding how expressions behave.

Your learners already know that when they have the expression $x-5$, it means there is a quantity of something, and it is decreased by 5.

Also, they already know that with the equation $x-5=6$, that the quantity is 11, through solving for $x$.

With factorising, an equation like $x^2-5x=0$ is initially rather difficult to solve.

After factorising out the x variable, $x(x-5)=0$, it now becomes much clearer which values (and there are two) make the equation true:

• Which values for $x$ make the left side of the equation equal to 0.

For emerging learners

At this stage, it’s helpful for learners to revisit common factors. Get used to listing the factors of each term and finding the highest common one. This is the value that will be factorised out of the brackets with the remaining amount left in the brackets:

$x^2-5x$

$x^2: x, x$

$5x:5,x$

Both terms have an  in common, so factorise that out of the brackets. The remaining factors stay inside the brackets.

$x(x-5)$

For learners needing extension

Revisit your work on expanding binomials. Look to see if you can discover a pattern for how to take your quadratic expression: $x^2-3x+2$ back to two sets of binomial expressions. There will be plenty of time to practice this and we will revisit this in the next newsletter.

At this point in S3, it’s helpful to focus on:

• Factorising quickly
• Knowing your tables – recalling them without having to count
• Finding the common factors with algebraic terms

S3 pupils who master this crucial skill have a much easier time when approaching new learning because of how closely related algebraic concepts are. These are exactly the kinds of ideas that make a noticeable difference when worked through carefully.

Each week, I’ll keep highlighting the key ideas that make the biggest difference as learners move through S3 along the National 5 pathway.

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