(6) Chap 5: Factorising ax^2 + bx + c

Look out for the approach... it's applying Grouping method

(5) Chap 5: Factorising x^2 + bx + c

By the Grouping Method...
Take note of the steps to 'break down' the middle term:

(4) Chapter 5: What does factorising x^2 + bx + c mean (visually)?

Reference: Worksheet 6a

Part 1:

LHS = a2 + 2a + 1
RHS = (a+1)(a+1), which can be rewritten as (a+1)2

Now, complete complete two other questions on the same page.

Part 2:
View the following animation to understand learn how the rectangular pieces are assembled.
Did you notice there is a systematic way of organising the rectangular piecs?

URL: http://staff.argyll.epsb.ca/jreed/math9/strand2/factor1.htm
Look at all THREE examples

Part 3:
Generate your own polynomials to factorise using the manipulatives
Update your diagrams and answers in the worksheet.

(a) Select "Tiles (Natural #)" to generate 3 polynomials

(b) Select "Tiles (Integers)" to generate 4 polynomials

(3) Chap 5: Watch the video... Factorisation by Grouping

Factorisation by Grouping: Look out for the approach!
  • Taking the terms by pairs first.
  • Identify the common factor between the 2 terms first.
  • Then carry out the same process - identify the common factor before putting the rest together.
  • The video also shows you that the same answer is obtained even if you re-organise the terms (sometimes)

Video 1:

Video 2:

(2) Chap 5: Factorisation by Identifying Common Factors

Listen carefully to the explanation. Two methods are presented.

(1) Chap 5: Factorisation... Watch the video...

As you watch the video, look out for the number that the expression was 'factorised'. Apart from identifying and removing the common factor, did you notice that it uses the algebraic identities to help factorise?
Useful identities:
  • (a+b)2 = a2 + 2ab + b2
  • (a-b)2 = a2 - 2ab - b2
  • (a+b)(a-b)2 = a2 - b2 
 Video 1

    Video 2