9.1 Add and Subtract Polynomials
Name ____________________
VERY IMPORTANT VOCABULARY!!!!!
 STANDARD FORM: terms are placed in
largest degree to
_____order, from the
degree (largest exponent, to smallest exponent)
 DEGREE: largest degree of the polynomials terms (look at the exponents!)
 LEADING COEFFICIENT: polynomial in standard form, the
___
of the _________ term
EXAMPLE: -4x2 + x3 + 3 - 5x4
Individual Terms: -4x2 , x3 , 3, -5x4
Standard Form: -5x4 + x3 – 4x2 +3
Degree: 4
Leading Coefficient: -5
Classification of Polynomials by number of terms
Classification
Definition
Example
Monomial
Polynomial with only _____
term
6
-2x
Binomial
Polynomial with _____ terms
3x + 1
4x3 – 5x
Trinomial
Polynomial with _______
terms
2x4 – 3x2 + 4
Practice: 1) Write the polynomial in standard form
2) find the degree 3)classify the polynomial by the number of terms
Standard Form
Degree
Name
2
3
1. 9x + 8x – 4x + 3
2. 5x + 6 – 3x3
3. –3x – 4x2
4. 5x3
Chapter 9 starts off with adding polynomials. You already know how to do this!
Circle the like terms:
5x
How do we add like terms?
2y
9x
3x2
5x + 2y + 9x + 3x2 =
Now, simplify each expression by combining like terms. Remember, DON’T
CHANGE THE EXPONENTS!
1.
8x  2y  3x
2.
 3x  7x
3.
6x 2  4x  3x 2
4.
x 2  9  6x 2
5.
6x2  3x  2x 2
6.
 4x 2  3x  7 x 2  8x
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Polynomial Addition:
Example:
(3x2 + 2x − 6) + (5x2 − 8x + 5)
Combine like terms:
You can also use Vertical Format:
3x2 + 2x − 6
+(5x2 − 8x + 5)
Practice:
1. ( 5x3 – x + 2x2 + 7) + ( 3x2 + 7 – 4x) + (4x2 – 8 – x2)
2. ( 2x2 + x – 5) + ( x + x2 + 6)
Polynomial Subtraction:
Change the – to a + and switch the signs of the terms in the second polynomial
think of it as _______________________________
Example: (3x2 + 2x − 6) - (5x2 − 8x + 5)
Switch from subtraction to addition and combine like terms:
Vertical Format:
Practice:
1. ( -2x3 + 5x2 – x + 8) – ( -2x3 + 3x – 4)
2. (x2 – 8) – ( 7x + 4x2)
3. (3x2 – 5x + 3) – (2x2 – x – 4)
4.
(5x2  3x  9)  (2x2  4x  2)
5.
( x2  3)
 ( 4x 2  7 )
Mixed Practice:
6.
7.
8.
(x2  7x  2)  (x2  5x  1)
(3x 2  5x  1)
 (4x 2  7x  2)
(2 x3  7 x 2  2)  ( x 2  5 x  1)
9.
(7x3  7x2  8)  (2x2  1)  (6x2  5x  2)
10.
Find the perimeter:
3 x- 5
4x - 6
2 x +4
Chapter 9 Vocabulary
Equation
Expression
Term
5x – 6 = 3x + 2
Mathematical sentence
formed by placing the
symbol = between two
expressions
Variable
2x – 3 or 5x
Combination of variables, #’s,
and operations
x2 – 5x + 6 ( 3 terms)
The parts of the
expression that are added
together
Exponent
Base
x, y , a
Letter used to represent
one or more numbers
34
34
Coefficient
Monomial
Degree of a Monomial
3x – 6
3x, 10, ½ ab2
Number part of a term
with a variable part
A number, a variable, or the
product of a number and one or
more variables with whole
number exponents
The sum of the exponents
of the variables in the
monomials
Polynomial
Degree of a Polynomial
Binomial
2x3 + x2 – 5x + 12
Is a monomial or a sum
of monomials
2x3 + x2 – 5x + 12
Degree: 3
The greatest degree of its
terms
6n4 – 5n2
Trinomial
Descending Order or Standard
Form
Not in standard form
15x – x3 + 3
Leading Coefficient
2x2 – x – 4
Polynomial with three
terms
Standard form:
-x3 + 15x + 3
Polynomial with two terms
2x3 + x2 – 5x + 12
Coefficient of the first
term
Example of a 2nd degree
Binomial
Example of a 3rd degree
Trinomial
Example of a 4th degree
monomial
x2 – 5x
a3 – a2 + 8
5x4