2ndF/3rdF Factorising and Solving Trinomials

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

Which exercises/theories shall we discuss on the board?

Recap: 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

Removing double brackets

Factorising trinomials

What do you notice?

Factorising trinomials

If a trinomial is of the form 

(so 1 in front of x-squared, a number in front of x and a single number)

then you can factorise the formula with double brackets

For the numbers on the dots you should find two numbers so that:

.... + .... = b                  the sum of the two numbers in the number in front of x

.... x .... = c                   the product of the two numbers is the single number

y=x​2​​+bx+c

y=(x+...)(x+...)

Factorising trinomials

Factorise 

Make a multiplication table.

We need two numbers on the dots

... + ... = 8

... x ... = 12

y=x​2​​+8x+12

Factorising trinomials

Factorise 

Make a multiplication table.

We need two numbers on the dots

2 + 6 = 8

2 x 6 = 12

So the factorised formula is 

y=x​2​​+8x+12

y=(x+2)(x+6)

Try it yourself!

Copy and make this exercise in your Notebook! 

Factorise 

Make a multiplication table.

We need two numbers on the dots

... + ... = ...

... x ... = ...

So the factorised formula is 

y=x​2​​+3x−18

SOLUTION:

Compare with your own work and

 correct, or add, if needed!

Factorise 

Make a multiplication table.

We need two numbers on the dots

6 + -3 = 3

6 x -3 = 18

So the factorised formula is 

y=x​2​​+3x−18

y=(x−3)(x+6)

Suppose.....

We have no 1 in front of the x squared!?

For example, How to: 

Solve -0.2 x squared + 3x - 10 = 0  ??!

Pokemon ??!

No:

Difficulty in MATH !!

Once more:

How to solve:

-0.2x squared + 3x - 10 =0 ?

First we multiply all terms on both sides of the = sign by -5!

You get:   x squared -15x + 50 = 0

NOW SOLVE THIS EQUATION IN YOUR NOTEBOOK! 

SOLVE:   x squared -15x + 50 = 0

SOLUTION:

(x - 10)(x - 5) = 0

x - 10 = 0  or  x - 5 = 0

x = 10  or  x = 5

Homework

Make and correct with your Solutionsbook:

REFRESH Ch 4, p.116/117

Good luck!