1. Review of Polynomials Term: 5x4 Exponent Numerical Coefficient
Variable or
(literal coefficient)

2. Polynomials
Type of Polynomial
Example
Number of terms
Degree
constant
Monomial
Binomial
Trinomial
5x2 1 2
2b3 + 5 2 3 5
x2 + 2x – 6 2
– 6 3
The degree is the value of the largest exponent.
The constant term is the one without a variable.

3. A polynomial must have exponents which are whole numbers
6x8 + 2x7 – 8x3 + 3x2 + 5x1 – 2
3x –2 – 2
Non-polynomials:

4. Like terms have the same variables
Unlike terms have the different variables 2a
– a 2a
– b 5x
– 4x2
5x2
– 4x2 12 –1 12
12x x3
– 2x3 x3
2x2

5. Example 1: Simplify fully.
Adding Polynomials
Example 1: Simplify fully.
(x2 + 2x + 5) + (3x2 – 4x – 2)
remove brackets
= x2 + 2x x2 – 4x – 2
add like terms
= x2 + 3x2 + 2x – 4x + 5 – 2
= 4x2 – 2x + 3

6. Subtracting Polynomials
Example 2: Simplify fully.
(2x2 + 4x + 1) – (3x2 + 5x – 3)
remove brackets
(signs change)
= 2x2 + 4x + 1 – 3x2 – 5x + 3
add like terms
= 2x2 – 3x2 + 4x – 5x
= – x2 – x + 4

7. Simplify each of the following.
a) (4x2 + 1) + (5 – 6x2)
b) (6x + 2) – (9x – 7)
= 4x – 6x2
= 6x + 2 – 9x + 7
= 4x2 – 6x
= 6x – 9x
= – 3x + 9

8. Multiplying Monomials Example: Simplify by multipling.1)
(4x5)(3x4)
= 12x9
multiply the coefficients, add the exponents 2)
(6y2)(2y3)(3y)
= 36y6 3)
(2z2)3
= 23z6
Power law: multiply the exponents
= 8z6 4)
(5a4)2
= 52a8
= 25a8

9. Expanding Polynomials
Distributive Law:
a(b + c) = ab + ac
Example: 8(x – 3)
(–3)(2x – 4)
= 8x
– 24
= – 6x
+ 12
a(3a + 2)
2p(4p2 + 5p – 3 )
= 3a2
+ 2a
= 8p3
+ 10p2
– 6p

10. Example:
2x(3x2 + 4x – 5)
= 6x3
+ 8x2
– 10x