1. 17.1 Understanding Polynomial Expressions
Students will learn to
Identify and classify polynomials
Write a polynomial in standard form

2. Vocabulary
Monomial
A number, a variable or the product of numbers and variables with whole number exponents
Degree of a Monomial
The sum of the exponents of the variables in the monomial
State the degree of each monomial
5 𝒙 𝟐 - 𝒂 𝟑 𝒃 𝟕 𝟐 𝟑 𝒘 𝒗 𝟒 𝒖 𝟓 𝟕

3. What do you think a polynomial is?

4. Polynomial A monomial or a sum of monomials
Which of the following are polynomials?
- 𝟑 𝟒 pq
𝟖 𝒕
5 – 6x
4 𝒙 −𝟑
-5 𝒙 𝟐 𝒚+𝟕𝒙+𝟐

5. Degree of a polynomial
The greatest degree of it terms
Standard form of a polynomial
Write with terms in descending order by degree
Leading coefficient
Coefficient of term with the highest degree
Constant term
Term whose variable has degree zero

6. 2 𝑥 3 −5𝑥𝑦+4𝑦+9 Example: Find the degree of each term.
2 𝑥 3 −5𝑥𝑦+4𝑦+9
degree 3
degree 2
degree 1
degree 0
Find the degree of each term.
Find the degree of the polynomial.
degree 3
Find the constant term. 9
Find the leading coefficient. 2

7. -4x + 9 - 𝒙 𝟐 −𝟐 𝒙 𝟕 Write in standard form. State the degree.
State the leading coefficient.
State the constant.

8. Classifying by degree Degree Classification Constant 1 Linear 2
Constant 1
Linear 2
Quadratic 3
Cubic 4
Quartic 5
Polynomial of degree 5 6
Polynomial of degree 6
etc

9. Classifying by terms Number of terms Classification 1 Monomial 2
Binomial 3
Trinomial
4 or more
Polynomial

10. Summary

11. Classify by terms and by degree.
3 𝑥 2 −5𝑥 9
−4 𝑥 3 +6 𝑥 2 +3x+7
5𝑥+3 𝑥 4 −2 𝑥 2

12. Turn to page 805 in your books

13. Homework
Page 812
#1-14, 17-19, 25