Factoring binomials

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• Middelbare school
• vwo
• Leerjaar 3

Factoring binomials

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f(x)=−3x​2​​+4x+3

f(x)=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

Find a, b and c in the formula

f(x)=−3x​2​​+4x+3

f(x)=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

a=−3

b=4

c=3

Solving with the quadratic formula

f(x)=−3x​2​​+4x+3

Solving with the quadratic formula

0=−3x​2​​+4x+3

Solving with the quadratic formula

0=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

Solving with the quadratic formula

0=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

a=−3

b=4

c=3

Solving with the quadratic formula

0=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

a=−3

b=4

c=3

x=​2 ⋅−3​​−4 ±√​4​2​​−4 ⋅−3 ⋅ 3​​​​​

Solving with the quadratic formula

                             or 

                    

0=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

a=−3

b=4

c=3

x=​2 ⋅−3​​−4 ±√​4​2​​−4 ⋅−3 ⋅ 3​​​​​

x=​−6​​−4+√​52​​​​​

x=​−6​​−4−√​52​​​​​

Solving with the quadratic formula

                             or

                             or

0=−3x​2​​+4x+3

x=​2a​​−b ±√​b​2​​−4ac​​​​​

a=−3

b=4

c=3

x=​2 ⋅−3​​−4 ±√​4​2​​−4 ⋅−3 ⋅ 3​​​​​

x=​−6​​−4+√​52​​​​​

x=​−6​​−4−√​52​​​​​

x ≈ −0,54

x ≈ 1,87

Remove the brackets

m(m−3)

1. 2m−3
2. m​2​​−3
3. m​2​​−3m
4. 2m−3m

Remove the brackets

m(m−3)

Quadratic formulas

c = 0

y=4x​2​​−8x+12

y=−x​2​​+25x

y=x​2​​

y=9x​2​​−13

y=−5x​2​​+2x

y=x​2​​+9x

y=3x​2​​−12x

y=−x​2​​−x

13.2: Factoring binomials

You can factorize (=make brackets) a formula  if c = 0. You have to find the biggest number and letter, that is a divisor of both terms

Example: Factor

You can divide both            and           by

Answer:

y=6x​2​​+4x

6x​2​​

4x

2x

y=2x(3x+2)

6x​2​​ : 2x=3x

4x : 2x=2

Example

Factor

16x​2​​−12x

Factor

18p​2​​+3p

7.2 Solving equations

                                    Example: Solve                                

Step 1, factorize: 

Step 2, make two equations:                                    or  

Step 3, use the balance method:                            or

Step 4, answer:                                                                or

15m​2​​+6m=0

3m(5m+2)=0

3m=0

5m+2=0

m=0

5m=−2

m=−​5​​2​​

m=0

Example

Solve                                 

2p​2​​+7p=0

Solve the equation

2x​2​​+8x=0

Solve the equation

2x​2​​+8x=0

Bettermarks

• Work on 13.2
  
• 20 min
• Raise your finger if you have any questions or when you're finished
  
• Communicate in English please

Question together

Ipads on the corner of the table

13.2 Question 16

Question 15

Bettermarks

• Work on 13.2
  
• Until the end of the lesson
• Raise your finger if you have any questions or when you're finished
  
• Communicate in English please