Algebra Honors

Adding and Subtracting Polynomials 8-1

VOCABULARY

Monomial: a constant, a variable or product of variables and WHOLE number exponents – one term

Binomial: The SUM of TWO monomials

Trinomial: The SUM of THREE monomials

Polynomial: a monomial or the sum of monomials

Degree of monomial: The sum of the exponents of all the variables in the term

Degree of polynomial: The highest degree of any term in a polynomial

Standard form  (Descending form): Place variables in alphabetical order with the highest power  first

Leading coefficient: The coefficient of the term that has the highest degree.

Degree	Name
0	constant
1	linear
2	quadratic
3	cubic
4	quartic
5	quintic
6	6th degree

ADDING AND SUBTRACTING POLYNOMIALS
This is nothing more than combining LIKE TERMS so this is DÉJÀ VU!

LIKE TERMS = same variable AND same power

You can do this using 3 different strategies:
1. Simply do it in your head, but keep track by crossing out the terms as you use them.
2. Rewrite, putting the like terms together (commutative and associative property)
3. Rewrite in COLUMN form, putting like terms on top of each other like you do when adding a column of numbers.

EXAMPLE OF COLUMN FORM:
[5x4 - 3x2 - (-4x) + 3] + [-10x4 + 3x3- 3x2 - x + 3]

Rewrite in column form, lining up like terms:
LEAVE A SPACE IF ONE OF THE POWERS ARE MISSING AND MAKE SURE BOTH OF THEM ARE IN DESCENDING ORDER!

                                                                                                                                          

                                5x4           - 3x2 - (-4x)  + 3                                                                        

                         + -10x4  + 3x3 - 3x2 -     x + 3                                                                                 

                           -----------------------------------                               

                              -5x4  + 3x3 - 6x2  + 3 x  + 6

SUBTRACTING POLYNOMIALS
You can use the ADDITIVE INVERSE PROPERTY (our BFF) with polynomials!
Subtracting is simply adding the opposite so.............
DISTRIBUTE THE NEGATIVE SIGN TO EACH TERM!!
(Change all the signs of the second polynomial!)
After you change all the signs,

use one of your ADDING POLYNOMIAL strategies!

EXAMPLE OF COLUMN FORM:
[5x4 - 3x2 - (-4x) + 3] - [-10x4 + 3x3- 3x2 - x + 3]
Rewrite in column form, lining up like terms:

                                                                                                                          

      5x4          - 3x2 - (-4x) + 3

- ( -10x4 + 3x3 - 3x2 -      x + 3)

        -----------------------------------
                                                                                                 

DISTRIBUTE THE NEGATIVE, THEN ADD:
                                                                                                                         

     5x4          - 3x2 -  (-4x) + 3   

+10x4 - 3x3 + 3x2 +      x - 3

                                ----------------------------------- 15x4 - 3x3    + 5 x