1. Polynomials
What are they anyway?

2. Monomials and Binomials
A MONOMIAL has only one term
e.g. 2x or 5y3 or -3a4 or 7
A BINOMIAL has two terms
e.g. 3x2 – 4
or a3 + 5
or x + 1
How many terms do you think a TRINOMIAL has?

3. Polynomials Polynomials contain more than one term
They include letters and numbers
They involve positive, whole number powers of the letters.
Division, square roots and negative powers cannot be involved.
The polynomial can include addition, subtraction and multiplication.

4. Which of these are polynomials?
8x2 + 3x – 2
8x-3 + 7y – 2
9x2 + 8x – 2 3
x3 + x2 + √x + 4
a4 + a3 – 2a2 + 3

5. Order of a Polynomial
The order of a polynomial is just the highest power of the letter in that polynomial
For example:
x4 – 5x3 + 6x – 4
Has order = 4

6. Multiplying Polynomials
You have been multiplying polynomials for a while – when you multiply out brackets!
If there are more than two terms in each bracket things become tricky so be careful
Make sure that everything in one bracket multiplies everything in the other.

7. Multiplying Polynomials
(x3 + 2x – 4) × (x2 – x + 3)
You could set the sum out like this if it helps:
x3 + 2x – 4
x x + 3
3x x – 12
-x x2 +4x
x x3 -4x2