1. Next week is revision week
What topics or objectives would you like to revise?

2. fACTORISING quadratics

3. What is a quadratic expression?
𝑎 𝑥 2 +𝑏𝑥+𝑐 𝑤ℎ𝑒𝑟𝑒 𝑎,𝑏 𝑎𝑛𝑑 𝑐 𝑎𝑟𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
In a quadratic expression, the HIGHEST POWER of 𝑥 is 2!

4. Expanding QUADRATIC EXPRESSIONS
Expand the following: (𝒙 +𝟒)(𝒙+𝟐) 𝒙 +𝟓 𝒙+𝟑 (𝒙 −𝟖)(𝒙−𝟒) (𝒙 −𝟑)(𝒙−𝟑)

5. Expanding QUADRATIC EXPRESSIONS
𝒙 𝟐 +𝟔𝒙+𝟖 𝒙 +𝟒
𝒙 𝟐
+𝟒𝒙 𝒙
(𝒙 +𝟒)(𝒙 +𝟐) x
+𝟐𝒙 +𝟖 +𝟐
𝒙 𝟐
+𝟐𝒙
+𝟒𝒙
+ 𝟖

6. Expanding QUADRATIC EXPRESSIONS
𝒙 𝟐 +𝟖𝒙+𝟏𝟓 𝒙 +𝟓
𝒙 𝟐
+𝟓𝒙 𝒙
(𝒙 +𝟓)(𝒙 +𝟑) x
+𝟑𝒙
+𝟏𝟓 +𝟑
𝒙 𝟐
+𝟑𝒙
+𝟓𝒙
+ 𝟏𝟓

7. Expanding QUADRATIC EXPRESSIONS
𝒙 𝟐 −𝟏𝟐𝒙+𝟑𝟐 𝒙 −𝟖
𝒙 𝟐
−𝟖𝒙 𝒙
(𝒙 −𝟖)(𝒙 −𝟒) x
−𝟒𝒙
+𝟑𝟐 −𝟒
𝒙 𝟐
−𝟒𝒙
−𝟖𝒙
+ 𝟑𝟐

8. Expanding QUADRATIC EXPRESSIONS
𝒙 𝟐 −𝟔𝒙+𝟗 𝒙 −𝟑
𝒙 𝟐
−𝟑𝒙 𝒙
(𝒙 −𝟑)(𝒙 −𝟑) x
−𝟑𝒙 +𝟗 −𝟑
𝒙 𝟐
−𝟑𝒙
−𝟑𝒙
+ 𝟗

9. Discuss with a partner what you think the method could be by observing these answers
fACTORISING
𝒙 +𝟐 𝒙+𝟒 = 𝒙 𝟐 +𝟔𝒙+𝟖 𝒙 +𝟓 𝒙+𝟑 = 𝒙 𝟐 +𝟖𝒙+𝟏𝟓 𝒙 −𝟖 𝒙−𝟒 = 𝒙 𝟐 −𝟏𝟐𝒙+𝟑𝟐 𝒙 −𝟑 𝒙−𝟑 = 𝒙 𝟐 −𝟔𝒙+𝟗

10. Observations 𝒙 +𝟐 𝒙+𝟒 = 𝒙 𝟐 +𝟔𝒙+𝟖
𝒙 𝟐 opens up as 𝒙 𝒂𝒏𝒅 𝒙
The signs are both plus
= +6
+ 2 x + 4 = +8

11. Observations 𝒙 −𝟖 𝒙−𝟒 = 𝒙 𝟐 −𝟏𝟐𝒙+𝟑𝟐
𝒙 𝟐 opens up as 𝒙 𝒂𝒏𝒅 𝒙
The signs are both negative inside the brackets but open up as – and +
= - 12
-8 x -4 = + 32

12. METHOD TO Factorise type1 quadratic 𝒙 𝟐 +𝟔𝒙+𝟖= 𝒙 +𝟐 𝒙+𝟒
𝑶𝒑𝒆𝒏 𝒖𝒑 𝒙 𝟐 as 𝒙 𝒂𝒏𝒅 𝒙, one in each bracket
Ask the Important Question:
Which TWO numbers give me +8 when I multiply them and +6 when I add them?

13. METHOD TO Factorise type1 quadratic 𝒙 𝟐 +𝟖𝒙+𝟏𝟓= 𝒙 +𝟑 𝒙+𝟓
𝑶𝒑𝒆𝒏 𝒖𝒑 𝒙 𝟐 as 𝒙 𝒂𝒏𝒅 𝒙, one in each bracket
Ask the Important Question:
Which TWO numbers give me +15 when I multiply them and +8 when I add them?

14. METHOD TO Factorise type1 quadratic 𝒙 𝟐 −𝟏𝟐𝒙+𝟑𝟐= 𝒙 −𝟒 𝒙−𝟖
𝑶𝒑𝒆𝒏 𝒖𝒑 𝒙 𝟐 as 𝒙 𝒂𝒏𝒅 𝒙, one in each bracket
Ask the Important Question:
Which TWO numbers give me +32 when I multiply them and -12 when I add them?

15. METHOD TO Factorise type1 quadratic 𝒙 𝟐 −𝟔𝒙+𝟗= 𝒙 −𝟑 𝒙−𝟑
𝑶𝒑𝒆𝒏 𝒖𝒑 𝒙 𝟐 as 𝒙 𝒂𝒏𝒅 𝒙, one in each bracket
Ask Important Question:
Which TWO numbers give me +9 when I multiply them and -6 when I add them?

16. Type 1 Quadratic: second sign + Bracket signs are THE SAME
What’s the shortcut?
Type 1 Quadratic: second sign +
Bracket signs are THE SAME
𝒙 𝟐 +𝟔𝒙+𝟖= 𝒙 +𝟐 𝒙+𝟒
𝒙 𝟐 +𝟖𝒙+𝟏𝟓= 𝒙 +𝟑 𝒙+𝟓
𝒙 𝟐 −𝟏𝟐𝒙+𝟑𝟐= 𝒙 −𝟒 𝒙−𝟖
𝒙 𝟐 −𝟔𝒙+𝟗= 𝒙 −𝟑 𝒙−𝟑

17. Factorise 𝒂 𝟐 +𝟏𝟎𝒂+𝟐𝟒 𝒂+𝟔 𝒂 +𝟒 𝒐𝒓 (𝒂+𝟒)(𝒂+𝟔) Ask Important Question:
𝑶𝒑𝒆𝒏 𝒖𝒑 𝒂 𝟐 as 𝒂 𝒂𝒏𝒅 𝒂, one in each bracket (𝒂 )(𝒂 )
Ask Important Question:
Which TWO numbers give me +24 when I multiply them and +10 when I add them?
6 and 4
𝒂+𝟔 𝒂 +𝟒 𝒐𝒓 (𝒂+𝟒)(𝒂+𝟔)

18. Factorise 𝒑 𝟐 −𝟏𝟔𝒑+𝟔𝟑
𝑶𝒑𝒆𝒏 𝒖𝒑 𝒑 𝟐 as 𝒑 𝒂𝒏𝒅 𝒑, one in each bracket (𝒑 )(𝒑 )
Ask Important Question:
Which TWO numbers give me +63 when I multiply them and −16 when I add them?
If when multiplied we get a positive number and when put together we get a negative number then BOTH numbers should be
NEGATIVE

19. Which TWO numbers give me +63 when I multiply them and −16 when I add them?
Factors of 63 −𝟏 × −𝟔𝟑 −𝟏−𝟔𝟑 = −𝟔𝟒 −𝟑 × −𝟐𝟏 −𝟑−𝟐𝟏 = −𝟐𝟒 −𝟕 × −𝟗 −𝟕−𝟗=−𝟏𝟔 𝒑 𝟐 −𝟏𝟔𝒑+𝟔𝟑=(𝒑−𝟕)(𝒑−𝟗)

20. STARS & WISHES What did you understand well about this lesson?
What do you wish to understand better?