QUADRATIC EQUATIONS : How to do Factorisation part.B (SPM, IGCSE, A-LEVEL...)

(Since my time is limited, so for every chapter I will skip some and only focus on parts which most of the students found problem with it. Maybe after I retire, then only I will complete those skipped parts.)

From now on which is part.B,
we will try to solve more complicated Factorisation questions,

First let's have a look at the question example:

The way of answering is still the same:

What is different than before,
is that the green part having two set of numbers to choose from,
which is 1&4 , 2&2.

Thus we need to see the middle blue part, the -3x to decide:

We can give up of 2&2,
since not matter how we play around with 2x & 2x also impossible to get -3x.

The final answer is:

Most of the things above are just explanation,
so actually I just need 1 row to get the Factorisation,
since most of it will be done in my brain:

First,
I will straight away write down x and x in the brackets:

That's how I did it within a line,
for more complicated one,
I will write down and do some calculations at one corner,
then only write down the final answer.

Let's have a look at another example:

Answer:

It seems like a lot of combinations,
but don't worry,
we still look at the middle blue part which is -10x.

The problem is,
not only 2&12,
but 4&6 also can plus/minus to get the -10x,
so we need to look back at the green part which is -24:

DONE.

Same like just now,
a simplified version of the solution:

Next,
let's do some practices,
not many, just 10 questions:

Same like last time,
I will not provide the answer.

Well,
because you just need to expand your answer,
see whether will you get back the same question,
then you will be able to find our whether your Factorisation is correct or not.

If you still find that Expansion is hard,
or you don't know how to expand easily,
please read:
https://leonmathstuition.blogspot.com/2019/02/quadratic-equations-before-learning.html

Let's continue with next example:

Answer:
(Since it is 0x, so there is no x at the middle, just add the +0x in it.)

OR!!!

If you still remember about the Expansion that you learnt in secondary lower,
you can do like this:

As usual,
10 questions to practice:

No answer provided,
so don't be lazy,
expand your answer to check.

Then.....................

I wonder do you all still remember the most basic Factorisation that you learnt long time ago,
where we could just Factorise the same thing out:

6x-3 = 3(2x-1)

This basic Factorisation is very important:

Answer:
(We will use the most basic Factorisation to factorise the same thing out first.)

DONE.

The last 10 questions to practice:

No answer will be provided.

That's all for today.

We will be entering part.C at next chapter,
which will be the final part of Factorisation.

Thank you!

End.

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Related articles:
Before learning Factorisation...
Factorisation part.A


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