Bell Work
3/23/2015
Simplify.
1.
4.
6.
y3
y5
3
 
 y
2.
a 3b6
a 7b
12 x5 y 9
3.
9 x8 y 4
4
 7x 
 
 5 
2
5.
9
 
 y
7.
x y 
 2 5
x y 
7
2
2
4
Heading
3/19/2016
7.6 Polynomials
Today we will find the degree and
classify polynomials in Standard
Form. Also identify the root of a
polynomial.
Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep problems, including word problems, by using
these techniques.
Notes
• Monomial
= a number, a variable, or a product of numbers
and variables with whole-number exponents.
- Monomials
7
x
9y
- Not Monomials
6x
2
9y  3
3xy
1
x
6x 2
.5x17
Notes
• Degree of a Monomial
= the sum of the exponents of the variables
- A constant has a degree of 0.
Find the degree of each monomial.
Ex.
Ex.
Ex.
3
8x
degree  3
7y
1
degree  1
13
degree  0
Ex.
6a 5b 2
degree  7
Now you try.
Ex.
Ex.
7
10c
degree  7
5 p
1
degree  1
Ex.
28
degree  0
Ex.
4x3 y 4 z 5
degree  12
Notes
• Polynomial
= An expression which is the sum of monomials.
• Degree of a polynomial
Ex.
5 x3  6 x 2  x  9
degree  3
• Standard Form
= Terms in order from greatest degree to least degree.
• Leading Coefficient
= The number in front of the first term when in
Standard Form.
Leading Coefficient  5
Notes
Write in standard form. Then give the leading coefficient.
Ex.
Ex.
3x  7  5 x3  4 x 2
 5x
5 x3 4x
4 x223x
3x77
8  4 x 4  x  3x9
4 x44xx88
3
3xx9  4x
LC  5
LC  3
Now you try.
Ex.
Ex.
6 x 2  2 x3  1  3x
3
 2x
2 x3 6x
6 x223x
3x1 1
LC  2
4 x  2 x 4  x 7  x 6
4
 x 77  x6  2x
2 x 4 4x
4x
LC  1
Notes
• Classifying Polynomials
• polynomials have specific names based on their
degree and the number of terms they have.
Degree
Terms
0
Name
Constant
1
Name
Monomial
1
Linear
2
Binomial
2
3
Trinomial
3
Quadratic
Cubic
Quartic
Polynomial
4
4 or
more
5
Quintic
6
6th degree
This is going to be our
CHEAT SHEET.
Notes
Classify each polynomial.
Ex.
Ex.
4 x3  5
Degree  3 , Terms  2
6 x  5x2  4
Degree  2 , Terms  3
Quadratic Trinomial
Cubic Binomial
Now you try.
Ex.
Ex.
7x 4
Degree  4 , Terms  1
Quartic Monomial
3x 2  7 x  1  x5
Degree  5 , Terms  4
Quintic Polynomial
Notes
• Root of a Polynomial
= the value for which the polynomial is equal to zero.
Tell whether each number is a root of the polynomial.
Ex.
Ex.
Ex.
3x 2  4 x  4; 2
2
 3 2   4  2  4
 3  4  8  4
 12  8  4
 44
0
Yes
Does it
equal zero?
x3  9; 3
3
  3  9
 27  9
 18
No
Does it
equal zero?
Now you try.
x 2  4;  2
2
 2  4
 44
8
No
Does it
equal zero?
Summary
Polynomials have special names based on the
degree and the number of ______.
terms First you have to
______
Standard Form. Then take the _______
highest
put it in _________
degree. Next count how many terms
_____ there are. The
root is the value that makes the polynomial zero.
____
Ticket Out the Door
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Classify each polynomial.
Ex.
7 x3  4 x  1
Degree  , Terms 
Today’s Homework
Rules for Homework
1. Pencil ONLY.
2. Must show all of your work.
• NO WORK = NO CREDIT
3. Must attempt EVERY problem.
4. Always check your answers.
Homework
7.6
Find the degree of each monomial.
3.
2.
6y
1.
3x 4
19
4.
4x3 y 5
Write in standard form. Then give the leading coefficient.
6.
 3x 2  x 7  6 x  2
5.
2 x  7  5 x3  2 x 2
Classify each polynomial.
8.
7.
6x  2
x3  2 x  6
9.
x2
Tell whether each number is a root of the polynomial.
10.
3x  12; 4
11.
x2  25; 5
12.
 3x 2  5 x  2; 2