QUADRATIC EQUATIONS : How to do Factorisation part.C (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,
we will enter part.C,
which is the last part of Factorisation.

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

Don't worry,
the way of doing is still the same.

Answer:

Since the 2 at the front can only come from 1x2,
so is 2x & x.

Since the 2 at the front is positive,
so 2x & x must be positive too.

Since 2x need to multiply with +1 to get +2x,
so 2x and +1 cannot be in the same bracket.

Same,
in order for x to multiply with -1 to get -x,
x and -1 cannot be in the same bracket also.

Thus:

A simplified version of the answer:

let's look at one more example:

Answer:

As usual,
the simplified version of answer:

One more example:

Answer:

Or you can use the below method:

Let's practice 10 questions before we entering the final stage:
：

No answer will be provided,
just expand it back to check!

Alright,
let's move on to the final stage.

Example:

Answer:

Which combination of numbers to choose from?

What we can rely now,
is our experience of doing Maths for all these years,
and our Maths sense.

If we picked the wrong combination of numbers,
we will realize something is wrong at the middle,
the most important thing is don't give up,
and choose another combination of numbers to do.

This time,
I choose 2x & 3x,
and 3&5.

Remember to expand back,
this is the best way to confirm your answer.

I met with students who are too lazy and unwilling to expand back to check answer,
which is not encouraged at all.

The simplified version of answer:

In order to be pro with Factorisation,
just remember that:

Expand back to check the answer!
Expand back to check the answer!
Expand back to check the answer!

Check by yourself,
find out what's wrong by yourself,
improve by yourself.

Never give up,
keep trying until you get the correct answer!

I also kept learning from my own mistake,
to be better at Factorisation.

Talked too much,
let's look at the last example:

Answer:

Done.

The last 10 questions for practicing:

No answer will be provided,
just expand it back to check.

That's all for the Factorisation,
we will be entering Completing The Square at next chapter.

Frankly speaking,
I am not very satisfied with this few chapters of Factorisation.

I feel like there is still a big gap between teaching directly comparing with teaching through the blog,
hopefully I will be able to improve and do it better next time.

Feel free to comment if you have any question or any parts which you don't understand.

Of course,
even if you understand all these,
it doesn't mean that you can get full marks in your exam.

UNDERSTANDING is just UNDERSTANDING,
SOLVING QUESTION is different.

At least if you understood,
it will help you a lot in solving questions.

Maths should be learnt easily,
Practice should be done accordingly,
exam should be faced seriously.

Thank you!

End.

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


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ABOUT ME
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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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ABOUT ME
MY MATHS BLOG(Chinese ver.)
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QUADRATIC EQUATIONS : How to do Factorisation part.A (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 we will be entering the topic of Factorisation.

First,
let's look at an example:

STOP!!!!

Like what I mentioned before,
teacher teach to let the students understand something,
not to teach to show off their knowledge,
so we should use a much simpler example:

So how to Factorise ?

Let's look at the Expansion from previous chapter:

Let me put some colours on it:

Did you realized that red parts on the left corresponded to the red on the right?
Also,
the green parts on the left corresponded to the green on the right?

Basically Factorisation is the reverse of Expansion:
(Explanation is included at below, you don't need to write so much when answering.)

RED : since we can only obtain x square from the multiplication of x and x.
GREEN : 7 can only be 1x7

Thus:

Then we think about how to add or subtract the green 1 and 7 to get the +8x at the middle:

+7x +1x = +8x

So the answer is:

Done.

After getting the Factorisation,
we can expand it back to check whether it is correct or not,
basically this type of question is like giving free exam marks for you.

Another example:

Answer:

Last example:

Answer:

The answer above actually included the explanation and some working process that we can do it in our brain,
so we don't need to write everything down during exam.

If excluding those,
I can actually answer in a line:

Next I prepared 10 questions,
please practice:

I will not provide the answer for the 10 questions above,
you just need to expand it back,
then you will know whether your answer is correct or not.

What?
Too troublesome to expand it back?

If you still don't know how to do Expansion in one line,
please read my previous chapter:
https://leonmathstuition.blogspot.com/2019/02/quadratic-equations-before-learning.html

If you still think that it is troublesome,
then I can only advice you not to be lazy.

That's all for today.

Please remember that this is just part.1,
next chapter will be part.2 .

Thank you!

End.

Please LIKE MY Facebook Page & FOLLOW MY TWITTER to be updated with the blog.


Related articles:
Before learning Factorisation...


Important Links:
CONTACT ME
ABOUT ME
MY MATHS BLOG(Chinese ver.)
MY YOUTUBE


Feel free to e-mail me if you have any problems:

leonleongmaths@gmail.com