Warm up
Combine Like Terms
1) 3x – 6 + 2x – 8
2) 3x – 7 + 12x + 10
5x – 14
15x + 3
Exponent Rules
3) What is 2x  3x?
6x2
Unit 1
Operations &
Rules
An expression that can have
constants, variables, &
exponents, but:
• No division by a variable
• Only whole number
exponents
 Named by their degree
 Named by their number of
terms
 Written in standard form
Polynomial
5x2y
– 3x + 10
-2y3 – 9
2
x
xy
5x
1
2
2
Degree of the Polynomial
Highest (largest)
exponent of the
polynomial
Standard Form
Terms are placed in
descending order by the
DEGREE.
Answers will always be
written in this form.
Degree
(largest exponent)
Name by
degree
0
Constant
1
Linear
2
Quadratic
3
Cubic
1. What is the degree name?
 2y  9
Linear
2. What is the degree name?
34x
3
Cubic
Adding
Polynomials
Drop the parenthesis &
combine like terms
3.
 2x
2
 
2

 4x  3  x  5x  1
2
3x
+x+2
4.
6  x    2 x  8 
2
2
x
+ 2x – 2
5. Find the perimeter of the rectangle.
3x  7
2x  1
10x + 12
Subtracting
Polynomials
Distribute the negative
& combine like terms
6.
 3a
2
3a
2
2
 

2
8a
+a
 10a  8a  a
+ 10a –
–
2
5a
+ 11a
7.
 3x
2
2
3x
2
 

2
2x
–x+1
 2x  4  2x  x  1
+ 2x – 4 –
2
x
+x–3
Multiplying
Polynomials
Distribute, follow exponent
rules, & combine like terms
8.
2
-2x(x –
3
4x + 2)
2
2 x  8 x  4 x
9.
(x + 3) (x – 3)
2
x 9
10.
(3x – 1)(2x – 4)
2
6 x  14 x  4
11. Find the area of the rectangle.
7x  10
4x  8
2
28 x  96 x  80
12. Find the volume.
x6
x3
x
3
2
x  9x  18 x
13. Profit Problem
The Profit, P(x) for a diving company is
represented by the product of the
revenue per dive, R(x), and the number of
customers, C(x).
If R(x) = 100 + 20x and C(x) = 30 – 2x, find
a polynomial representing P(x).
2
40 x  400 x  3000
Homework
Practice
Worksheet