1. Maths – Core 2 – Algebraic Division
(and Remainder theorem)

2. I bet all of you lot forgot how to do long division, SO I’m
gonna remind you how….
E.G - 145,650 ÷4
So we write it out like this
4 145, 650
So we have 4, and we
want to see how many 4 145, 650
of those can fit into
145,650
We split the large number
4 14-56-50 into smaller ones which
we can easily use so we
can divide much more
easily.

3. each time we go down
we’re going to split the
numbers again differently.
You’ll see why :P
36412.5
4 14-56-50
-12
025-65-0 So 4*6 = 24, the 24 is
taken away from 25 giving
-24 us 1 and the 6 goes on top
So now that we have 50 16-50 The 16 is completely
left on it’s own, we can -16 divisible by 4 so it goes on
top but we have nothing
divide it by 4, which will
give us 12.5, which can 00-50 left so we move over to the
50
now be added on to the
top and our answer is
complete

4. Algebraic Division, works pretty much in the same
way….
E.G 4x³ + 2x²+ 3x + 5 ÷ (x +2)
Set it out the same way
(x+2) 4x³ + 2x²+ 3x + 5
AND SOLVE BITCH SOLVE
(just kidding I’ll show you how :P)

5. So ignoring the +2 (because
it will sort itself out)
We need to know how many
-25
times x can go into
4x³, which is 4x² etc…
4x²-6x+15x+(x+2)
we then
1. Add that to the top as (x+2) 4x³+2x²+3x+5
part of out answer 4x² (x+2) -(4x³+8x²)
2. Times it by (x+2)
3. Take away the expanded
brackets 0+(-6x²+3x)
4. Repeat process for the
next few..
-6x (x+2)
-(-6x²-12x)
Just like normal division
Note: If the trinomial has a 0+15x+5
part of the sentence not
included, you should add the
15x (x+2) -(15x + 30)
omitted part e.g
4x³ + 2x²+ 5 ÷ (x +2) 0 -25
When you go to solve it, it
should be written as….
Woah, what’s this? We have a
(x+2) 4x³ + 2x²+ 0x + 5
remainder????, Yes we take it to the top
This will make solving it much
and divide it by (x+2) and add it on
easier

6. Remainder Theorem
This is basically a way of finding out the remainder, MUCH FASTER!!!
When we have to divide 4x³ + 2x²+ 3x + 5 by (x+2). But they only want the value
of the remainder, there are much quicker ways of going about this.
Well there’s this little saying, (To be honest with
When f(x) divides by (ax+b) you, I have no idea
The remainder is -b what that means :L)
f a
But in essence, what you do is, you get b and
(x+2) = (ax+b)
substitute –b into x into the trinomial
So –b= -2
4x³ + 2x²+ 3x + 5
Use a becomes
calculator, it 4*(-2)³+2*(-2)²+ (3*-2)+5
really helps :P
And then Solve!!, so 4*(-2)³+2*(-2)²+ (3*-2)+5 = -25
-25, as you know so well, was the remainder in the previous
example (just to show you it works)