1. Polynomials
Algebra

2. Objective
Today you will find the degree of a polynomial and write polynomials in standard form

3. A polynomial is a monomial or the sum of monomials, each called a term of the polynomial. Some polynomials have special names. A binomial is the sum of two monomials. A trinomial is the sum of three monomials

4. Monomial, binomial, or trinomial?
Identify Polynomials
Expression
Is it a polynomial?
Monomial, binomial, or trinomial?
4y – 5xz
YES! 4y – 5xz is the sum of two monomials 4y and -5xz
binomial
-6.5
YES! is a real number
monomial
7a-3 + 9b
NO! 7a-3 is NOT a monomial
6x3 + 4x + x + 3
YES! 6x3 + 4x + x + 3 = 6x3 + 5x + 3, the sum of three monomials
trinomial

5.  YOUR TURN! 
Is it a polynomial? If yes, identify as monomial, binomial, or trinomial. x
YES! Monomial
b) -3y2 – 2y + 4y – 1
YES! Trinomial
c) 5rx + 7tw
YES! Binomial
10x-4 – 8ax
NO! 10x-4 is not a monomial and 8ax has a variable exponent.

6. The degree of a monomial is the sum of the exponents of all its variables. A nonzero constant has degree 0. Zero has no degree. The degree of a polynomial is the greatest degree of any term in the polynomial. To find the degree of a polynomial, you must find the degree of each term.

7. 6th degree, 7th degree, and so on
Name
constant 1
linear 2
quadratic 3
cubic 4
quartic 5
quintic
6 or more
6th degree, 7th degree, and so on

8. Degree of a Polynomial Find the degree of each polynomial. 3a2b3 + 6
Step 1: Find the degree of each term
3a2b3: degree = 2 + 3= 5
6: degree = 0
Step 2: The degree of the polynomial is the greatest degree, 5

9. Degree of a Polynomial Find the degree of the polynomial.
2d3 – 5c5d – 7
2d3: degree = 3
- 5 c5d: degree = = 6
-7: degree = 0
The degree of the polynomial is 6

10.  YOUR TURN!  Find the degree of each polynomial: 7xy5z 7
b) 2rt – 3rt2 – 7r2t2 – 13 4

11. The standard form of a polynomial is written with the terms in order from greatest degree to least degree. When a polynomial is written in standard form, the coefficient of the first term is called the leading coefficient. 4x3 – 5x2 + 2x is the leading coefficient 3 is the greatest degree

12. Standard Form of a Polynomial
Write each polynomial in standard form. Identify the leading coefficient.
3x2 + 4x5 – 7x
Step 1: Find the degree of each term
Step 2: Write the terms in descending order
4x5 + 3x2 – 7x
The leading coefficient is 4

13.  YOUR TURN! 
Write the polynomial in standard form and identify the leading coefficient.
8 – 2x2 + 4x4 – 3x
4x4 – 2x2 – 3x L.C. = 4
y + 5y3 – 2y2 – 7y6 + 10
-7y6 + 5y3 – 2y2 + y L.C. = -7

14. A snail can sleep for three years.
Thought of the Day!
A snail can sleep for three years.