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

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

What do you think a polynomial is?

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

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

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

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

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

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

Summary

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

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

(6xy + 3x – 9y) + (5x + 8y – xy)

𝒙 𝟐 −𝟕𝒙+𝟗 +(𝒙 −𝟒 𝒙 𝟑 −𝟒)

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

(5 𝒙 𝟐 −𝟗𝒙+𝟑) −(𝟒𝒙 −𝟕 𝒙 𝟐 )

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)

During the period 1999-2005, the number of hours a person watched broadcast television B and cable television C can be modeled by B = 2.8 𝒕 𝟐 −𝟑𝟓𝒕 + 879 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?

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

Time to practice 1.http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/sprac_a.htm 2. http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/sprac_s.htm 3. http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/sprac_m.htm 4.http://www.regentsprep.org/Regents/math/ALGEBRA/AV2/sapplied.htm 5.http://teachers.henrico.k12.va.us/math/hcpsalgebra1/Documents/examviewweb/ev7-5.htm

Homework Page 557-559: #2-28 even, 30, 31, 34, 35, 37, 38, 40