1. What 2 numbers add to give the first number and multiply to give the second number …
e.g. 11 & 30 the two numbers are: 5 and 6 because
6 & =11 & 5×6=30
9 & 14.
9 & 18.
7 & 10.
10 & 21.
11 & 10
11 & 28
13 & 40
13 & 36
11 & 24
1 & -6
1 & -12
4 & -21
7 & -18
2 & -24
1 & -30
2 & -35
6 & -27
-1 & -20
-4 & -12
-4 & -21
-5 & -50
-8 & -9
-4 & -45
-5 & -24
-4 & -5

2. Factorising (One Bracket)
7x+7y=
8x+12=
3x+x2=
12x2+6x=
p2q3-pq2=
18xy2-12x2y2=

3. Expanding
(x+3)(x-6)
FOIL is a mnemonic used for expanding quadratic expressions (2 brackets)
F=First O=Outer I=Inner L=Last
(first ______)(first_____) (x+3)(x-6)
(outer______)(_____outer) (x+3)(x-6)
( _____ inner)(inner _____) (x+3)(x-6)
( ______last)( ______ last) (x+3)(x-6)

4. Factorising (2 Brackets)
Factorising is the reverse of Expanding. You are finding the factors.
(x+4)(x-2) = x2+2x-8
What two numbers multiply to give -8 and add to give +2?
x2+8x what two numbers multiply to give
and add to give
+3 and +5
So x2+8x+15 factorised is (x+3)(x+5) or (x+5)(x+3)
You do: Factorise a) x2+9x+14
(x+4)(x-2)=
+4 and -2
Factors of 15 are
1×15 & 3×5

5. One positive factor & one Negative factor…
x2 + 2x – 24
Two numbers that multiply to give -24 and add to give +2.
Write down all the factors of 24: -1×24, -2×12, −3×8, -4×6,
1×-24, 2×-12, 3×-8, 4×-6.
Which pair add to give +2?
These are our factors.
x2 + 2x – 24 = (x-4)(x+6)
Your Turn:
x2 + 3x - 40