This is a comprehensive pack of notes about grade 9 factorization. It teaches about factors, difference of two squares, trinomial factorisation, grouping to create a common factor-bracket, trinomials with a common factor, and factorising involving the change in sign rule. It contains notes, example...
FACTORISATION
containing manyterms as
expression
> Factorisation is the process of rewriting an
an expression that is a single term. distributive lawand
of the of
> Factorising an expression is the reverse piprocess "answer" is a product
which means that the final
multiplication (i.e. F.0.1.L.),
factors and factor-brackets:
’ (...)x(...X..)
question says "multiply and simplify" we have to REMOVE
wnentne
BRACKETS; this creates many terms.
question says "factorise" we have to CREATE a product of
wien rne
BRACKETS; becoming a single term.
do usually
The type of factorising youterms in the
depends on the number of
expression!
TYPES OF FACTORISING NUMBER OF TERMS NEEDED
Firstly:
Taking out the highestcommon factor (HCF) (2 or more terms)
4 Grouping... to create a common factor-bracket (4 or more terms)
Secondly:
Difference of two squares (DOTS) (2terms only)
Thirdly:
Trinomial (3 terms only)
OTE. Sometimes acombination of factoising
methods will need to be used. When
tackling these problems, attempt to factorise in the prescribed order above
, FACTORS
> Afactor is nuumber/expression without a
Something that divides into a
remainder.
Example:
Factors of 24 are 1,2,3. 4,6, 8, 12 and24.
Factors of xy are x, y and xy. 2x²y, y, 2y
Factors of 2xy are 1, 2, x,x,xy,xy, 2x, 2x*, 2xy,
Mathematics
Complete: Exercise 18.1 (page 235) Classroom
TAKING OUT THE HIGHEST COMMON FACTOR[HGH
*2 OR MORE TERMS ARE NEEDED
> Find all the factors of each term in the expression.
common factor of each term.
P Kewrite each term bringing out the
Take out the common factor.
(the remainder-bracket).
Rewrite what remains of each term in a bracket
> e.g.1 Factorise 8ak- 6bk
factorise each term.
= 2.4. a. k- 2.3. b. k
= 2k. 4a-2k. 3b bring out the common factor.
=2k(4a - 3b) divide each term by the common factor.
yousee
magical 1... now
a
> e.g.2 Factorise x - 2x + x coefficientofxis
The
youdon't. taken out.
= X.x-x. 2x +x.1 it.. now when the HCF is
becomes visible
= x(x*-2x+ 1) It
Note: There are 3 terms in the
remainder-bracket which is the same
as the original number of terms.
When the first term is
negative, or all terms
e.g.3 -a'b'c + 2ab²ç3- ab'c? are negative, we usually
= -ab'c². abc² + ab'c². 2c - ab'c²,1 take out a - sign with the
Common factor.
-ab²c² (abc' - 2c + 1)
The HCF is the lowestexponent of Notice the signs of the
terms in the
the variable that is common toALL
the terms.
remainder
bracket all change.
193 | Page
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller sofiafrenchza. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.95. You're not tied to anything after your purchase.
