2TH §11.1 Factorising

• Wiskunde
• Middelbare school
• havo
• Leerjaar 2

What will we do today...

• Questions about the homework? R3 until R9 (skip R6)
• Recap terms and factors
• Recap sum and product
• Recap prime numbers
• We do together: Ch 11: Exercises R1 and R2
• Homework: Ch 11.1 Do Exercises 3, 4, 6, 7, 8
• Exit ticket

Which exercises should we discuss on the board?

Recap: terms and factors

In the formulas:        

 y = 2x + 5           p = 7t - 1           

2x and 5       &    7t and -1          &                      and                    are called terms.

terms are the "parts" you add up.

In the formula 

3, x and 2 are called factors.

factors are the "parts" you multiply

c=10h−2h​2​​

10h

−2h​2​​

y=3⋅x⋅2

Recap: Sum and Product

The sum of 2 and 5 is 7.           (2 + 5 = 7)

The sum means you add up the terms.

The product of 2 and 5 is 10.      (2 x 5 = 10)

The product means you mulitply the factors.

What is the product of 12 and 3?

1. 4
2. 9
3. 15
4. 36

Prime factorisation

Prime numbers are numbers that can only be divided by 1 AND by itself and still have a whole number as a result.

2, 3, 5, 7, 11, 13, 17, ... are prime numbers, because they only have 1 and itself as divisors

12 is not a prime number, because it has 1, 2, 3, 4, 6 and 12 as divisiors.

Prime factorisation

You can write a number as a product of as many prime factors as possible:

12 = 2 x 2 x 3

21 = 3 x 7

50 = 2 x 5 x 5

80 = 2 x 2 x 2 x 2 x 5

Prime factorisation

How can you write a number as a product of prime factors?

Option 1: 

Write the number as a product of two numbers

Write each of the the tow numbers as a product of two smaller numbers

Repeat untill you only have prime factors.

280 = 10 x 28

280 = 2 x 5 x 2 x 14

280 = 2 x 5 x 2 x 2 x 7

Prime factorisation

How can you write a number as a product of prime factors?

Option 2: 

Divide by the smallest prime number (2) as often as possible

Divide by the next prime number (3) as often as possible

Repeat for 5, 7, 11, etc

280 : 2 = 140                       

140 : 2 = 70                        

70 : 2 = 35                        

Prime factorisation

How can you write a number as a product of prime factors?

Option 2: 

Divide by the smallest prime number (2) as often as possible

Divide by the next prime number (3) as often as possible

Repeat for 5, 7, 11, etc

280 : 2 = 140                      

140 : 2 = 70                         35 : 5 = 7 (also a prime number)

70 : 2 = 35                         280 = 2 x 2 x 2 x 5 x 7

Factorising terms with variables

You can also factorise a term such as                   or 

by writing the number as a product of prime factors and writing the variable part as a product of variables:

15x​2​​

15x​2​​=3⋅5⋅x⋅x

8a​3​​

8a​3​​=2⋅2⋅2⋅a⋅a⋅a

HW Thursday

§11.1 Do Exercises 3, 4, 6, 7, 8

Check your answers with the Solutions book at home.

Exit ticket