1. 9.1 Add and Subtract Polynomials
Students will learn to
Identify and classify polynomials
Write a polynomial in standard form
Add/subtract polynomials

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. To add or subtract polynomials combine like terms
Arrange the terms in columns of like variables and combine the like terms.
(3x - 4 𝒙 𝟐 +𝟖) +(𝟐 𝒙 𝟐 −𝟕𝒙+𝟐)
-4 𝒙 𝟐 +𝟑𝒙+𝟖
2 𝒙 𝟐 −𝟕𝒙+2
-𝟐 𝒙 𝟐 −𝟒𝒙+10

14. (6xy + 3x – 9y) + (5x + 8y – xy)

15. 𝒙 𝟐 −𝟕𝒙+𝟗 +(𝒙 −𝟒 𝒙 𝟑 −𝟒)

16. When subtracting distribute the negative and add like terms.
(5x + 9 𝒙 𝟐 −𝟖) −( 𝒙 𝟐 +𝟐𝒙 −𝟒)

17. (5 𝒙 𝟐 −𝟗𝒙+𝟑) −(𝟒𝒙 −𝟕 𝒙 𝟐 )

18. Simplify: (𝒅 𝟐 −𝟖𝒅+𝟒)+(𝟓𝒅 −𝟑)+(𝟕− 𝒅 𝟐 )
(𝒅 𝟐 −𝟖𝒅+𝟒)+(𝟓𝒅 −𝟑)+(𝟕− 𝒅 𝟐 )
(−𝟕𝒂 𝟐 −𝒂+𝟒)−(𝟔𝒂 −𝟐 𝒂 𝟐 )+(𝟑 𝒂 𝟑 −𝟔)

19. During the period , the number of hours a person watched broadcast television B and cable television C can be modeled by
B = 2.8 𝒕 𝟐 −𝟑𝟓𝒕 and C = -5 𝒕 𝟐 +𝟖𝟎𝒕+𝟕𝟏𝟐
where t is the number of years since 1999.
Write a model in simplified form to express the total number of hours people watched television.
About how many hours did a person watch in 2012?

20. Write a simplified expression to represent the perimeter of the triangle.

21. Time to practice 1. 2. 3. 4. 5.

22. Homework
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#2-28 even, 30, 31, 34, 35, 37, 38, 40