Division with polynomials

1
Division with polynomials

• Missing number games
• Reverse table method
• Its just like Sudoku

2
Finding one bracket given the other
Fill in the empty bracket
x2 - x - 20 (x 4)( )
x2 - x - 20 (x 4)(x )
x2 - x - 20 (x 4)(x - 5)
Expand it to check (x 4)(x - 5) x2
4x - 5x -20 x2 - x - 20
3
We can do division now
f(x) (x2 - x - 20) ? (x 4)
(x 4) x f(x) (x2 - x - 20)
4
Finding one bracket given the other - cubics
x3 3x2 - 12x 4 (x - 2)(x2 )
x3 3x2 - 12x 4 (x - 2)(x2 -2)
x3 3x2 - 12x 4 (x - 2)(x2 5x -2)
5
Finding one bracket given the other - cubics
(2.1)
Using a multiplication table
x3
3x2
-12x
4
x3
4
Can put x3 and 4 in. They can only come from
1 place. So a 1, c -2
6
Finding one bracket given the other - cubics
(2.2)
Using a multiplication table
3x2
-12x
-2x
x3
-2x2
4
7
Finding one bracket given the other - cubics
(2.3)
5x
Using a multiplication table
3x2
-12x
bx2
-2x
x3
-2x2
-2bx
4
Gather like terms
Either way, b 5
8
Have a go

• Page 87
• Exercise E
• 1, 2, 3

9
Dealing with remainders
remainder
Using a multiplication table
x3
Can put x3 This can only come from 1 place. So a
1
10
Dealing with remainders
x2
remainder
Using a multiplication table
x3
-x2
x
x3
15
bx2 2x2 -x2
b 2 -1
b -3
11
Dealing with remainders
x2 -3x
remainder
Using a multiplication table
x3
-x2
x
x3
15
-3x2
2x2
cx - 6x x
c - 6 1
c 7
12
Dealing with remainders
x2 3x 7
remainder
Using a multiplication table
x3
-x2
x
7x
x3
15
-3x2
-6x
2x2
13
Dealing with remainders
x2 3x 7
remainder
Using a multiplication table
x3
-x2
x
7x
x3
15
-3x2
14
-6x
2x2
Remainder
The numerical term (15) comes from the 14 and
the remainder R
15 14 R
So, R 1
14
Dealing with remainders
x2 3x 7
Using a multiplication table
x3
-x2
x
7x
x3
15
-3x2
14
-6x
2x2
Remainder
The numerical term (15) comes from the 14 and
the remainder R
15 14 R
So, R 1
15
Homework (For Tuesday 18th Oct)

• Page 86
• Exercise D
• Q5, 6, 7
• Exercise E
• Q4 - rearrange first
• Q6 (a)(i)