This document discusses division of polynomials. It explains that division is the opposite of multiplication and involves calculating a quotient and remainder. It shows examples of dividing numbers and polynomials, identifying the divisor, quotient, and remainder. It also introduces the "Big L" method for polynomial long division, which involves arranging the terms in a particular way to calculate the quotient and remainder.

1. Block 2
Divisors, Quotients and
Remainders

2. What is to be learned?
• What divisors, quotients and remainders
are.
• How to divide poLynomials

3. Division
Opposite of multiplying
3 X 6 = 18
so 18 ÷ 3 = 6
20 ÷ 3 = 6 r 2
Divisor Quotient
D Q R

4. 37 ÷ 5 = 7 r 2
23 ÷ 4 = 5 r 3
x2
+ 6x + 5 ÷ (x – 2)?
x2
+ 6x + 5 = (x – 2)
37 = 5 X 7 + 2
D Q R D Q R
23 = 4 X 5 + 3
(x + 8) + 21
D Q R
xx22
+ 6x + 5 ÷ (x – 2) = (x + 8) + 21+ 6x + 5 ÷ (x – 2) = (x + 8) + 21
DD Q RQ R

5. 37 ÷ 5 = 7 r 2
23 ÷ 4 = 5 r 3
x2
+ 6x + 5 ÷ (x – 2)?
x2
+ 6x + 5 = (x – 2)
37 = 5 X 7 + 2
D Q R D Q R
23 = 4 X 5 + 3
(x + 8) + 21
D Q R
xx22
+ 6x + 5 ÷ (x – 2) = (x + 8) + 21+ 6x + 5 ÷ (x – 2) = (x + 8) + 21
DD Q RQ R

6. 37 ÷ 5 = 7 r 2
23 ÷ 4 = 5 r 3
x2
+ 6x + 5 ÷ (x – 2)?
x2
+ 6x + 5 = (x – 2)
37 = 5 X 7 + 2
D Q R D Q R
23 = 4 X 5 + 3
(x + 8)+ 21
D Q R
xx22
+ 6x + 5 ÷ (x – 2) = (x + 8) + 21+ 6x + 5 ÷ (x – 2) = (x + 8) + 21
DD Q RQ R
More Useful

7. The Big L to the Rescue!
x2
+ 6x + 5 ÷ (x – 2)
1 6 5

8. The Big L to the Rescue!
x2
+ 6x + 5 ÷ (x – 2)
1 6 52
1
2
8
16
21
xx22
+ 6x + 5 ÷ (x – 2) = (x + 8) + 21+ 6x + 5 ÷ (x – 2) = (x + 8) + 21
DD Q RQ R
D
RQ
(x + 8) + 21xx22
+ 6x + 5 =+ 6x + 5 = (x – 2)
D RQ
x +

9. 3x3
+ x2
– 6x + 2 ÷ (x – 5)
3 1 -6 25
3
15
16
80
74
D
RQ
(3x2
+ 16x + 74) + 3723x3x33
+ x+ x22
– 6x + 2=6x + 2=(x – 5)
D RQ
370
372
x3
x2
x no.
x2
x no.

10. Division of PoLynomials
using The Big L
20 ÷ 3 = 6 r 2
so 20 = 3X 6 + 2
Divisor Quotient
D X Q +R
Remainder
(also known as synthetic division)

11. For PoLynomials
2x3
+ x2
– 6x + 7 ÷ (x – 3 )
2 1 -6 73
2
6
7
21
15
D
RQ
(2x2
+ 7x + 15) + 522x2x33
+ x+ x22
– 6x + 7=6x + 7=(x – 3)
D RQ
45
52
x3
x2
x no.
x2
x no.

12. Dead Important
÷ (x + 4)

13. Dead Important
÷ (x + 4)
-4

14. 3x3
+ x2
– 6x + 7 ÷ (x + 2)
3 1 -6 7-2
3
-6
-5
10
4
D
RQ
(3x2
– 5x + 4 ) – 13x3x33
+ x+ x22
– 6x + 2=6x + 2=(x + 2)
D RQ
-8
-1
Key Question