POLYNOMIALS
POLYNOMIALS
A math equation consisting of one to many
terms.
Examples:
6, x, 6x,
-1/2xy, 2y + x,
x2 – 5x - 9
Polynomials cannot have a variable as a
denominator nor negative exponents.
Are the following polynomials?
7/a
¼ xy – 10
3pq1/2
√7 x4 – x3
8-2
Polynomials with
• one term are called monomials
5x3, 8, x2, etc
• two terms are called binomials
3x – 1, 2x2 + 8, etc
• three terms are called trinomials
2x2 – 4x + 9
• Variables – a letter that represents one
or more numbers
4y = y is the variable
• Coefficient – number in front of a
variable
4y = coefficient is 4
DEGREES OF A POLYNOMIAL
The degree of a polynomial is the degree
of the term with the highest exponent.
Constant term: term without a variable.
2x – 1 = degree of 1 Constant term of -1
These are called a linear.
2x2 + 8 = degree of 2 Constant term of 8
These are called quadratic.
2x3 – 5 = degree of 3 Constant term of -5
These are called cubic.
EXAMPLE 1
State the degree, coefficient’s and
constant term of the polynomial.
5x3 + x2 – 7x + 9
EXAMPLE 2
State the degree, coefficient and constant
term of the polynomial.
6a – 4a2 - 3
ADDING AND SUBTRACTING POLYNOMIALS
Find like terms and combine them in order
to simplify polynomials.
4x – 2x2 + 3 – 6x2 + 5 – x
TRY THE FOLLOWING
a2b – ab2 + 4a3b – 7ab2 + 5a2b
(3a – 4b + c) + (3b – 5c – 3a)
BE CAREFUL WITH SUBTRACTION
(4x2 – 9x + 6) – (2x2 – 3x – 1)
Work on Handout
FACTORING LINEAR POLYNOMIALS
Just as natural numbers can be factored
so can polynomials.
Find the GCF in each term and then factor.
FACTORING EXAMPLES
4m + 12
GCF = 4
= 4 (m + 3)
6 – 15a
GCF = 3
= 3 (2 – 5a)
TRY THE FOLLOWING
6n + 9 =
6c + 4c2 =
3g + 6 =
8d + 12d2 =
FACTORING TRINOMIALS
ax2 + bx + c
5 – 10z – 5z2
Find the GCF of all three terms.
In this example the GCF is 5.
Factor out a 5 from each and write as a product.
5 ( 1 – 2z – z2)
EXAMPLES
18a2 – 12a + 6
9 + 27x – 45x2
FACTORING WITH MORE THAN ONE VARIABLE
Find all GCF’s, numbers and letters.
-12 x3y – 20xy2 – 16x2y2
GCF for numbers = 4
GCF for letters = 1x and 1y
4xy (-3x2 – 5y – 4xy)
5ab2 + 10a2b3 – 15a2b4
-
20c4d - 30c3d2 – 25cd
Work on textbook questions # 6, 7, 8, 9,
10, 14.