8-1 Solving by factorising

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

8-1 Solving by factorising

What you need: - Textbook, writingbook, iPad - Pen, pencil, geotriangle - Calculator

Schoolbags in the cuboard

Phones in the phonebag

Bluetooth 

- ON

- VPN off

                         Lesson goals

• Solve equations with factorisation.
• Factorize a difference of two squares.

A x B = 0

In this case A = 0 or B = 0

A quadratic equation is not written in the form A x B = 0 can be solved by factorising.

Solve the following equations:

a

1. x=0 or x=-4
2. x=0 or x=4
3. x=0 or x=-2
4. x=0 or x=2

b

1. x=0 or x=-3
2. x=0 or x=3
3. x=0 or x=-1/3
4. x=0 or x=1/3

c

1. x=0 or x=-2,5
2. x=0 or x=2,5
3. x=0 or x=-5
4. x=0 or x=5

d

1. x=3 or x=6
2. x=3 or x=-6
3. x=-3 or x=-6
4. x=-3 or x=6

e

1. x=7 or x=2
2. x=-7 or x=2
3. x=7 or x=-2
4. x=-7 or x=-2

f

1. x=3 or x=5
2. x=-3 or x=5
3. x=3 or x=-5
4. x=-3 or x=-5

5a

1. y=x​2​​−21
2. y=x​2​​−10x−21
3. y=x​2​​+10x−21
4. y=x​2​​+4x−21

5b

1. y=x​2​​−9
2. y=x​2​​+9
3. y=x​2​​−6x+9
4. y=x​2​​−3x+9

5d

1. y=x​2​​−25
2. y=x​2​​+25
3. y=x​2​​−50x−25
4. y=x​2​​+50x+25

5e

1. y=x​2​​+4
2. y=x​2​​−4
3. y=x​2​​−8x−4
4. y=x​2​​+8x+4

Factorizing a difference of squares

x​2​​−81=0

(x−9)(x+9)=0

x−9=0

x+9=0

or

x=9

x=−9

8a

1. x=-10
2. x=0 or x=10
3. x=0 or x=-10
4. x=10 or x=-10

8b

1. x=0 or x=-9
2. x=9 or x=9
3. x=9 or x=-9
4. x=9

8c

1. x=0 or x=-1
2. x=-1
3. x=1
4. x=1 or x=-1

8d

1. x=4 or x = -4
2. x=0 or x = -4
3. x=4
4. x = -4

Try on your own

1, 2, 5 and 7

RULES:

• In your writingbook
• Use: Textbook
• Discussion when you are stuck is allowed

Extra excercise: 4

Challenge: 6, 7

Homework: 3, 7, 9 (p. 38)

If you forgot what cards are, look on page 37 of the textbook.