factorising trinomials

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Factorising

Today we will learn...

How to factorise a trinomial

a + b

a x b

4x + 8 = 4 (x+2)

3x + 5

3a + 4b + 2c

Sum

product

factorisation

binomial

trinomial

which two numbers have a product of 20 and a sum of 9?

1. 10 and 2
2. 3 and 6
3. 4 and 5
4. 20 and 9

Which two numbers have a product of 20 and a sum of 21?

1. 10 and 2
2. 20 and 1
3. 4 and 5
4. 20 and 21

Which two numbers have a product of 20 and a sum of -12?

1. 10 and -2
2. 10 and 2
3. -10 and -2
4. -10 and 2

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. 

Removing double brackets

Factorising trinomials

What do you notice?

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=x​2​​+bx+c

y=(x+...)(x+...)

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=x​2​​+8x+12

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=x​2​​+8x+12

y=(x+2)(x+6)

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=x​2​​+3x−18

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=x​2​​+3x−18

y=(x−3)(x+6)

let's practice!

Do exercise 26. check your answers.

All correct? Go straight to 31

Any mistakes? go to 27.

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

Words I've learned today...