Polynomials
What are they anyway?
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?
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.
Which of these are polynomials?
+ 3x – 2
 8x-3 + 7y – 2
 9x2 + 8x – 2
3
 x3 + x2 + √x + 4
 a4 + a3 – 2a2 + 3
 8x2
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
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.
Multiplying Polynomials
(x3 + 2x – 4) × (x2 – x + 3)
You could set the sum out like this if it helps:
x3 + 2x – 4
x2 - x + 3
3x3
+ 6x – 12
-x4
-2x2 +4x
x5
+2x3 -4x2