2TH §11.2 Factorising binomials

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

Plan for today

New theory: Factorising binomials

Homework: §11.2: Exercises S14, 15 and S17

Last 20 minutes:Discussing test Chapter 9

Which exercises shall we discuss on the board?

Recap: factorising terms

You can factorise terms like this:

30x​2​​=2⋅3⋅5⋅x⋅x

22a​3​​=2⋅11⋅a⋅a⋅a

12b=2⋅2⋅3⋅b

Binomials and Trinomials

A formula like                                 is called a binomial

(bi = 2, the formula has 2 terms)

A formula like                                           is called a trinomial

(tri = 3, the formula has 3 terms)

y=3x​2​​+6x

y=x​2​​+7x+10

Largest common factor

A common factor is a factor that two terms have in common.

                               are common factors for the two terms.

The largest common factor of these terms is 

12x​2​​=2⋅2⋅3⋅x⋅x=4x⋅3x

8x=2⋅2⋅2⋅x=4x⋅2

4x

2,4,2x,4x

Factorising binomials

You can factorise a binomial, by filling in a multiplication table in reverse:

1) find the largest common factor:

y=9x​2​​−21x

What is the largest common factor of
and

9x​2​​

21x

1. 3
2. 3x
3. 6x
4. 9x​2​​

Factorising binomials

You can factorise a binomial, by filling in a multiplication table in reverse:

1) find the largest common factor:                              &      

2) make a multiplication table. Fill in the binomial inside the table and the largest common factor in the left column.

3) Fill in the missing factors

y=9x​2​​−21x

9x=3x⋅3x

21x=7⋅3x

Factorising binomials

You can factorise a binomial, by filling in a multiplication table in reverse:

1) find the largest common factor:                            &      

2) make a multiplication table. Fill in the binomial inside the table and the largest common factor in the left column.

3) Fill in the missing factors

4) Write as a product of factors

y=9x​2​​−21x

9x=3x⋅3x

21x=7⋅3x

Factorising binomials

You can factorise a binomial, by filling in a multiplication table in reverse:

1) find the largest common factor:                              &      

2) make a multiplication table. Fill in the binomial inside the table and the largest common factor in the left column.

3) Fill in the missing factors

4) Write as a product of factors

y=9x​2​​−21x

9x=3x⋅3x

21x=7⋅3x

y=3x(3x−7)

Try it out

Factorise the binomial

Take a photo of your solution in your notebook.

 

a=24t​2​​+16t

Factorise the binomial

a=24t​2​​+16t

Try it out

Factorise the binomial

Solution: 

 

a=24t​2​​+16t

a=8t(3t+2)

Homework

§11.2 Do Exercises S14, 15 and S17

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