Solving by factorising jko

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Solving by factorising TVWO 2

                         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 that 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

a

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

b

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

c

1. y=x​2​​−14x−49
2. y=x​2​​+49+14x
3. y=x​2​​+49x+49
4. y=14x​2​​+x+49

d

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

e

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

f

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

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

a

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

b

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

c

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

d

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

Challenge: zero flaws...

Write down the area of 

segments I, II and III

The area of the tiled path is

34m^2.

How wide is the tiled path

1. 34 m
2. -17m
3. 17m
4. 2m

x​2​​+15x=34

x​2​​+15x=34

x​2​​+15x−34=0

x​2​​+15x=34

x​2​​+15x−34=0

(x−2)(x+17)=0

x​2​​+15x=34

x​2​​+15x−34=0

(x−2)(x+17)=0

x−2=0orx+17=0

x​2​​+15x=34

x​2​​+15x−34=0

(x−2)(x+17)=0

x−2=0orx+17=0

x=2orx=−17

so the answer is 2

x​2​​+15x=34

x​2​​+15x−34=0

(x−2)(x+17)=0

x−2=0orx+17=0

x=2orx=−17

                         Lesson goals

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