**Problem**

**Introduction**

This problem was posed by a student going
on to Secondary 1 (~ grade 7) next year. This sort of problem is usually done at
Secondary 2 or 3 (about grade 8 or 9). This
reminds me of my personal story.

I accidentally discovered quadratic
equations when I was in Primary 4. I
imagined a rectangle whose length is 2
cm longer than the breadth. If the breadth is 4 cm, the length is 6 cm and the area is obviously 24 cm². But if I pretended that I knew the area but
did not know the dimensions, I did not know how to solve it with the knowledge
that I had at that time. This started me
on a quest to find out the answer. I
read secondary school guidebooks, asked my friend’s brothers and sisters, and even
asked my Chinese teacher (who, after exams, offered to answer any question we
had)! Basically, I was offered two
choices: (1) trial and error factorisation and (2)
the quadratic formula. I did not like guess
and check (or hit and run?), and the quadratic formula looked formidable to me.

So I
started a quest to find a method of

*factorisation*that did not require trial-and-error. By secondary 1, after fiddling around with algebra, I managed to do it. I reconstruct my derivation below. And then I use my method to solve the above factorisation problem.**Derivation**

**Solution**

**Remark**

This looks like a Pyrrhic victory. But like they say, it’s the journey and not
the destination that matters. Doing my
own explorations prepared me for future learning and made me understand better.

Nowadays, the new models of calculators
give solutions to the associated equations and you can work backwards to get the
factorisation. Unfortunately, many students
just blindly use this and forget to work backwards, giving the wrong factorisation.
If calculator gives 9 and

^{-248}/_{29}, and you write your factorisation as (*x*– 9)(*x*+^{248}/_{29}), your answer is wrong. Moral of the story: you still need to use your brain.
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