1. Warm-Up #23 (Monday, 10/26) Simplify (x+2)(3x – 4)
2. Simplify (x+2)( x 2 −3x−1)
3. Factor 16x 2 −25

2. Homework (Monday, 10/26)
lesson 2.06_page 98 #11, 12, 13

3. Lesson 2.06 Anatomy of a Polynomial

4. Monomial
A monomial is the product of a number, the coefficient, and one or more variables raised to nonnegative integer powers.
If a monomial has more than one variable, the degree is the sum of the exponents of each variable
Example:
3𝑥 2
6𝑛 3 𝑦 4

5. Polynomial
A polynomial is a monomial or a sum of two or more monomials
Each term contains only variables with whole number exponents and real number coefficients
Examples:
3x + 7
7𝑥 2 −5𝑥+3
2 𝑥 4 𝑦 3 + 3𝑥𝑦 2

6. Standard Form
A polynomial is in standard form when its terms are written in descending order of exponents from left to right
Examples:
2x + 7
14𝑐 3 −5𝑐+8
4𝑎𝑏 2 −3𝑎𝑏+2

7. 𝟑𝒙 𝟑 − 𝟓𝒙 𝟐 −𝟐𝒙+𝟏 Parts of a polynomial Cubic term Linear term
Quadratic term
Constant
Leading
coefficient

8. Degree of the Term
The exponent of the variable in the term determines the degree of the term
Example:
The highest degree of 12𝑑 5 is 5 or fifth degree
What is the highest degree of 14𝑐 3 ?
Since the exponent is 3, then the term is of degree three or cubic.
What is the highest degree of 14𝑐 c + 3?
This is third degree, or cubic, polynomial since the highest exponent is 3.

9. You Try: What is the highest degree and leading coefficient for each polynomial
14𝑐 𝑐 2 −𝑐+1
3𝑐+ 2𝑐 2 −1
𝑐 𝑐 1 −3𝑐+6
4𝑐 𝑐 4 −2𝑐
d: c:

10. Classifying Polynomials by Number of Terms
Example
Number of Terms
Name
14c 1
Monomial
2c – 7 2
Binomial
14𝑐 2 +8𝑐 −5 3
Trinomial
14𝑐 𝑐 2 −𝑐+1 4
polynomial
ANYTHING MORE THAN A MONOMIAL IS CONSIDER A POLYNOMIAL

11. Classifying Polynomials by Degree
Example
Degree
Name 14
Constant
2x – 7 1
Linear
14𝑥 2 +8𝑥 −5 2
Quadratic
14𝑥 3 +16 3
Cubic
14𝑥 4 +7𝑥−2 4
Quartic
−4𝑥 5 − 𝑥 3 5
Quintic

12. Recognize Degree
There is no special name after the 5th degree. You only write it as 6th degree, 7th degree, etc.
The degree determines how many possible solutions/x-interceptions the function can have.

13. Classifying the Polynomial
Write each polynomial in standard form and classify it by degree and number of terms
5𝑥 3 +4𝑥+ 2𝑥 2 +1
7𝑥 5 + 3𝑥 3 −2𝑥+4

14. Find a polynomial (an example) that satisfy each condition
Find a polynomial (an example) that satisfy each condition. If it is impossible to satisfy the condition, explain why.
A cubic polynomial with three terms, all of different degrees
A linear polynomial with two terms, both of different degrees
A linear polynomial with three terms, all of different degrees

15. Is each result always a polynomial? Explain
Sum of two polynomials
Product of two polynomials
Difference of two polynomials
Quotient of two polynomials