This document provides instructions on how to factorize quadratic expressions into their prime factors. It includes the following steps: - Factorize expressions of the form ax^2 + bx + c by finding two terms whose product is a and sum is b. - Always expand the factors to check the factorization is correct. - To factorize expressions with negative constants, list the factors of the constant term and try different pairings with the variables until expanding checks. - More complex expressions may require trial and improvement to find the correct factors.

1. Factorisation
By the end of the lesson you will be able to:
• Factorise quadratic expressions(trinomials) of
the form: ax2
+bx+c

2. Factorise fully:

3. Factorise fully:

4. Let's try to factorise
Which two terms multiply to make ?
2x2
+7x+5
( ) ( )
2x2
( ) ( )
Now, to make the :5
( ) ( )
2x
x
2x
x
+1 +5
Let's expand:
2x2
+10x+x+5
2x2
+11x+5

5. ( ) ( )2x
x
+1 +5
We have to swap around the 1 and the 5
Now, expand again:
Always expand to check !!!!!!

6. Factorise:
3x2
+16x+21
( ) ( )
List the factors of 21:
so it could be:
(3x +7) ( x + 3)or(3x +3) ( x + 7)
Expand to see which is the correct one. So
3x2
+16x+21 = (3x +7) ( x + 3)

7. Let's try to factorise 3x2
+13x­10
( ) ( )
List the factors of -10:
The best way to find the correct pair is trial and
improvement

8. Now even worse!
4x2
­4x­3
Which two terms multiply to make ?4x2
It could be:
or(4x ) ( x ) (2x ) ( 2x )
List the factors of -3:
Now try the different possibilities until you find the
correct one

9. Factorise:
4x2
­25

10. solve worksheet "Factorisation " Ex D2

11. 2 x3
­ 11 x2
+ 5x=
At the end of the lesson:
Factorise: