1. Expression Term Equation Coefficient Identity Function Polynomial Root
Lesson Objective Understand the meaning of the words:
Be able to simplify polynomials, extend to adding, subtracting, multiplying and dividing them
Expression
Term
Equation Coefficient
Identity
Function
Polynomial
Root
Be able to manipulate polynomials

2. Expression Term Equation Coefficient Identity Function Polynomial Root
An algebraic statement made up of variables and numbers with their respective powers along with a some mathematical operations of any type
An statement consisting of variables and numbers with their respective powers that are only multiplied or divided
An expression that contains an equals sign
The number part of a term
A statement of equivalence between two expressions that is always true for the same inputted value
Another name for a formula
An expression that can be simplified so that it contains only terms in one variable with positive whole number powers
The name given to a solution of an equation

3. Expressions, Terms, Coefficients and Polynomials
An expression is a mathematical ‘sentence’. It contains terms that are separated by + and – signs.
A term is a ‘word’ in the ‘sentence’.
Eg 3x2 – 4y + 2x + 3xy – 4x2y + 2y +
Expressions that are of the form:
a0xn + a1xn-1+ a2xn-2 + a3xn-3 + ………….. + an-1x + anx0
are called polynomials

4. 3x2 + 2xy – 3y xy
How many terms?
What is the coefficient in x2?
What is the coefficient in y?
What is the coefficient in ?
What is the constant term?
Which of the following expressions are polynomials?
2x3 + x2 + x b) 3x + 1 c) 6
3x + x-5 e) sin(x) + 2 f) x3
g) x7 + 1/2x5 - 3x h) i) π

5. Lesson Objectives: Simplify:
Be able to simplify polynomial expressions
Be able to add, subtract and multiply polynomial expressions
Simplify:
3x + 4x2 – 2y + 3y -4x + 5x2 + 2xy – 3yx + 5x2y

6. Expressions are simplified by collecting together ‘like terms’
‘Like terms’ are those that contain exactly the same letters and powers
Eg Simplify 3x + 2xy + 4x + 3yx + 2x2
Simplify 5xy2 + 3xy + 2yx + 2x2y + 3xy2
Simplify 3x + 2y – 4x + 3 – 5x2 – 3x2 + 4y + 7

7. Simplify:
3x + 4y - 2x + 6y
3 – 4x x
2x + 3x2 – 3x – x2
2y + 3y – 4x – 5y + x
3xy + 2yx + 3x – 5y – 6x – 2yx
7x2 + 3x + 4x – 5x2 + 2x
2x2 – 3x + 2x2y + 3xy – 4yx2 – 2x2 – 5yx
3x + 2x2 – 4x + 3x2 – 2x + x
-5xy + 3yx + 2xy – xy + x + 3x
2x2 + 3x – 4x2 – 3x + x2 – 2x + 3x2

8. Multiplying Polynomials
A= 2x C = 3x - 5
B = 3x2 – 2x – 5 D = 2x2 + x – 4
Find:
A + C b) A + B c) A – B
d) AC e) A2 f) C2
D - B h) 2A - C i) BC
j) BD k) A + BD l) B2
m) A3 n) AD – BC o) A ÷ D

9. Multiplying Polynomials
A= 2x C = 3x - 5
B = 3x2 – 2x – 5 D = 2x2 + x – 4
Find:
A + C b) A + B c) A – B
d) AC e) A2 f) C2
D - B h) 2A - C i) BC
j) BD k) A + BD l) B2
m) A3 n) AD – BC o) A ÷ D
5x - 2
3x2 - 2
-3x2 + 4x + 8
6x2 – 9x - 15
4x2 + 12x + 9
9x2 – 30x + 25
-x2 + 3x + 1
X + 11
9x3- 21x2- 5x+ 25
15x4- x3- 24x2 + 3x +20
6x4- x3- 24x2 + 5x +23
9x4- 12x3- 26x2 + 20x + 25
-5x3 + 29x2 - 37
8x3 + 36x2 + 54x + 27

10. Lesson Objectives:
Dividing polynomials
Common misconceptions:

11. Dividing Polynomials
Find ÷ 4
What about
( ) ( ) ÷ ? .

12. Find the missing factor if:
Divide by
Divide by .

13. + - × ÷ x2+5x - 6 x + 3 2x3- x2 x - 1 3x2+8x+4 x2 + x x2 + 4x + 3
We need to be able to accurately add, subtract, multiply and divide expressions:
x2+5x - 6
x + 3
2x3- x2
x - 1
3x2+8x+4
x2 + x
x2 + 4x + 3
x3+ 2x2- 4x + 1
x3+ 3x2+ 3x + 1
x + 1 + - × ÷

14. Lesson Objective
Factorising single and double brackets

15. Find
1) (x + 2)(x + 5) 2) (2x + 1)(x + 4)
3) (x2 – 3)(x2 + 2x + 4) 4) (x + y)(2x – 3y + 4)
5) (2x4 – 2x2 + 3x – 5) ÷ (2x + 1)

16. 4x – ) 9x + 12
3) 8x – ) 12x – 9
4x2 + 2x 6) 9x2 – 6x
7) 12x2 + 15x 8) 12x + 8x2
20x – 15x ) 8xy + 12x2y
11) 8x2y – 6xy ) 9x2 – 27x + 12
13) x2 + 7x ) x2 + 9x + 20
15) x2 – 7x – ) x2 + 3x – 18
x2 – ) x2 + 7x – 18
19) x2 + x – ) x2 - 64

17. 21) 2x2 + 5x ) 3x2 + 5x + 2
23) 2x2 + 9x ) 5x2 + 6x + 1
25) 2x2 + 7x ) 3x2 + 9x + 20
27) 3x2 + 10x ) 7x2 + 23x + 6
29) 4x2 + 4x ) 4x2 + 5x + 1
31) 4x2 – ) 16x

18. Lesson Objective the Remainder Theorem

19. 3x + 4 = 2x – 6 2(3x + 1) = 6 + 2(x – 1) ½(x + 6) = x + 1/3(2x – 5)
Page 10 and 11 Exercise Book