factorising trinomials

Factorising
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Slide 1: Carte mentale
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Factorising

Slide 1 - Carte mentale

Today we will learn...
How to factorise a trinomial

Slide 2 - Diapositive

a + b

a x b
4x + 8 = 4 (x+2)
3x + 5

3a + 4b + 2c
Sum
product
factorisation
binomial
trinomial

Slide 3 - Question de remorquage

which two numbers have a product of 20 and a sum of 9?
A
10 and 2
B
3 and 6
C
4 and 5
D
20 and 9

Slide 4 - Quiz

Which two numbers have a product of 20 and a sum of 21?
A
10 and 2
B
20 and 1
C
4 and 5
D
20 and 21

Slide 5 - Quiz

Which two numbers have a product of 20 and a sum of -12?
A
10 and -2
B
10 and 2
C
-10 and -2
D
-10 and 2

Slide 6 - Quiz

Factorising trinomials
  • Factorising means to write as a product.
  • For trinomials, we use brackets to do this. 
  • Factorising is the opposite of multiplying out the brackets. 

Slide 7 - Diapositive

Removing double brackets

Slide 8 - Diapositive

Factorising trinomials
What do you notice?

Slide 9 - Diapositive

Factorising trinomials
If a trinomial is of the form 
(so 1 in front of x-squared, a number in front of x and a single number)
then you can factorise the formula with double brackets

For the numbers on the dots you should find two numbers so that:
.... + .... = b                  the sum of the two numbers in the number in front of x
.... x .... = c                   the product of the two numbers is the single number
y=x2+bx+c
y=(x+...)(x+...)

Slide 10 - Diapositive

Factorising trinomials
Factorise 
Make a multiplication table.

We need two numbers on the dots
... + ... = 8 (the sum is 8)
... x ... = 12 (the product is 12)
which two numbers have a sum of 8 and a product of 12?
y=x2+8x+12

Slide 11 - Diapositive

Factorising trinomials
Factorise 
Make a multiplication table.

We need two numbers on the dots
2 + 6 = 8
2 x 6 = 12
So the factorised formula is 
y=x2+8x+12
y=(x+2)(x+6)

Slide 12 - Diapositive

Try it yourself!
Copy and make this exercise in your Notebook! 

Factorise 
Make a multiplication table.

We need two numbers on the dots
... + ... = ...
... x ... = ...
So the factorised formula is 
y=x2+3x18

Slide 13 - Diapositive

SOLUTION:
Compare with your own work and
 correct, or add, if needed!

Factorise 
Make a multiplication table.

We need two numbers on the dots
6 + -3 = 3
6 x -3 = 18
So the factorised formula is 
y=x2+3x18
y=(x3)(x+6)

Slide 14 - Diapositive

let's practice!
Do exercise 26. check your answers.
All correct? Go straight to 31
Any mistakes? go to 27.

Slide 15 - Diapositive

Write down in your own words how to factorise a trinomial.

Slide 16 - Question ouverte

Words I've learned today...

Slide 17 - Carte mentale