Objectives:
Add and Subtract polynomials
Use polynomials to model real-life situations

Polynomial: a monomial or the sum or difference of two
or more monomials. (exponents are nonnegative integers)

Standard form: the form of a polynomial that places the
terms in descending order by degree

Degree of a monomial: the sum of the exponents of the
variables of each term

Degree of Polynomial: the highest degree of any term of
the polynomial

Leading Coefficient: the coefficient of the first term of a
polynomial written in standard form

Classified by number of
terms:

Classified by degree:


Monomial is one term


Binomial is two terms


Trinomial is three terms

Polynomial is four or more
terms


Constant is a single
number with degree 0
Linear is a polynomial of
degree 1
Quadratic is a polynomial
of degree 2
Cubic is a polynomial of
degree 3
Quartic is a polynomial of
degree 4
Polynomial
x2  6
5  9y
4 w3  8w  9
4 y 4 z
7 y  2 y3  3 y 4  y 2
4.3
Degree
Leading
Classify by
Coefficient Degree
Classify by
terms

To add or subtract polynomials, add or subtract
the like terms and write the answer in standard
form.

To add or subtract polynomials, you group like
terms and add their coefficients.

EX:
3
3
5
r

8

6
r

   3
3
3
5
r

8

6
r

   3
2
2
x

4
x

3

3
x

   3x  5

1.

2
2

4

3
x

x

2
x
2. 
   x  1


3.
4.
2
3
2
5
x

2
x

1

4
x

3
x
 6x  2

 
2
2
2
x

7
x

3

3

2
x

9
x

 

2
2
3
12
x

8
x

6


8
x

4
x
 14 

 

5.

4
2
3
2
3
9
x

x

7
x

x

6
x

2
x

9

4
x
6. 
 
   3x  8 

Projected from 1950 through 2010, the total population P
and the male population M of the United States (in
thousands) can be modeled by the following equations,
where t is the number of years since 1950

TOTAL population model:
MALE population model:


P  2387.74t  155, 211.46
M  1164.16t  75,622.43
Find a model that represents the female population F of
the United States from 1950 to 2010.
20 questions