Download multiplying monomials

Algebra 1: 8-4
POLYNOMIALS
8-4 Algebra 1
Polynomial – a monomial or a sum of
monomials. Remember, it is not a monomial
if there is a variable in the denominator, so it
cannot be a polynomial either. That means, you
cannot have a variable with a negative power … that would put
the variable into the denominator.
A binomial is the sum of two monomials.
A trinomial is the sum of three monomials.
Examples: State whether each expression is a
polynomial, and identify it as a monomial, binomial
or trinomial.
5x
_________
6m2
4z + 6
_________
3x + 2yz ________
2m – 3n + 4x-1
__________
___________
5a + 2b – 3a + 6m
______________
… careful … combine like terms first!
Pg 1
G. Kelly
Algebra 1: 8-4
Degree of a monomial – the sum of the
exponents of all its variables.
monomial
8m3
7x
-4xy3z2
5
degree
Degree of a polynomial – the greatest degree
of any term in the polynomial. The degree
is found by getting the sum of the exponents
of all the variables within a single term.
Example: 6a2b3 ……. degree is 5
3x2y3 + 4r3d7 – 5xy2 …. so degree is 10
degree: 5
10
3
4x2y – 2xy + 3y – 4 …. so degree is 3
degree: 3
2
1 0
Pg 2
G. Kelly
Algebra 1: 8-4
Ascending order means from least to
greatest (increasing).
Descending order means from greatest to
least (decreasing)
Arrange the terms of each polynomial so
that the powers of x are in ascending order.
15 + 14x3 + 2x – x2  15 + 2x – x2 + 14x3
0
3
1
2
2xy3 + 7y2 + 4x3 – x2y2
1
0
3
2
 7y2 + 2xy3 – x2y2 + 4x3
Arrange the terms of each polynomial so
that the powers of x are in descending order.
8 + 7x2 –12xy – 4x3y  -4x3y+7x2 –12xy+8
0
2
1
3
ax2 + a4 – 2a3xy3 – 9x4y  you try
Pg 3
G. Kelly
Algebra 1: 8-4
Vocabulary you need to know:
term: a number, a variable, or a product/
quotient of numbers and variables. To
determine the number of terms in an
expression use this definition: anything
separated by a plus or minus sign.
variable: a letter or a product of letters.
coefficient: the number in front of a variable
(or product of variables).
constant term: a number all by itself (no
variable with it)
4x2y – 2xy + 3y – 4
Number of terms:
List of terms:
variables:
coefficients:
constant term:
Pg 4
4
4x2y, – 2xy, 3y, – 4
x2y, xy, y
4, -2, 3
-4
G. Kelly
Algebra 1: 8-4
3x2y3 + 4r3d7 – 5xy2 – y2 + 6
Number of terms: 5
List of terms:
3x2y3, 4r3d7, -5xy2 , -y2, 6
variables:
x2y3, r3d7, xy2 , y2
coefficients:
3, 4, -5, -1
constant term: 6
2x3– 3x2 + x3 + 6x3y – z2 – 10 – 5x2
 careful!! … combine like terms first!!!
Number of terms: _______
List of terms:
__________________
variables:
___________________
coefficients:
___________________
constant term: ________
Pg 5
G. Kelly