1. Polynomials
CA 10.0

2. Objective - To classify polynomials and write them in standard form

3. MONOMIALS Monomial - A single term. A group of
numbers and/or variables tied
together by multiplication or
division but separated by
addition or subtraction.
single
Examples:
Coefficient - The number preceding a variable
in a variable term.

4. MONOMIALS
The DEGREE OF A MONOMIAL is the sum of the exponents of the variables.
Example:
To find the degree, ADD the exponents!
2+4=6
The degree is 6.
4 is a constant. Constants have a degree of 0
The invisible exponent is 1. The degree is 1.

5. POLYNOMIALS Polynomial - A variable expression
consisting of many terms
that can’t be combined.
many
Examples:

6. Polynomials
The DEGREE OF A POLYNOMIAL is the degree of the term with the greatest degree.
The highest degree is 1, so the degree of the polynomial is 1.
The highest degree is 3, so the degree of the polynomial is 3.
The highest degree is 4, so the degree of the polynomial is 4.

7. POLYNOMIALS
The terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in STANDARD FORM.
The STANDARD FORM OF A POLYNOMIAL that contains one variable is written with the terms in order from the greatest degree to the least degree.

8. POLYNOMIALS
Re-write these in standard form:

9. POLYNOMIALS
When a polynomial is written in standard form, the coefficient of the first term is called the LEADING COEFFICIENT.
Examples:
The leading coefficient is 5.
The leading coefficient is 1.

10. POLYNOMIALS
Some polynomials have special names based on their degree and the number of terms they have.
DEGREE:
NAME: 1 2 3 4 5
6 or more
Constant
Linear
Quadratic
Cubic
Quartic
Quintic
6th degree, 7th degree, …

11. POLYNOMIALS TERMS: NAME: 1 2 3 4 or more Monomial Binomial Trinomial

12. POLYNOMIALS Classify each polynomial: Degree: 3, Terms: 1
Cubic Monomial
Degree: 2, Terms: 3
Quadratic Trinomial
Degree: 9, Terms: 2
Ninth degree Binomial

13. POLYNOMIALS 25 ≠ 0, so 4 is NOT a root of
A ROOT of a polynomial in one variable is a value of the variable for which the polynomial is equal to 0.
Example: Tell if the number is a root of
25 ≠ 0, so 4 is NOT a root of

14. POLYNOMIALS 0=0, so –1 is a root of
Example: Tell if the number is a root of
0=0, so –1 is a root of