Warm Up Jan. 28th 1. 2. 3. 4. 5.

Polynomials A polynomial is a monomial or a sum of monomials Example: x3 + xy + y2

Classifying Polynomials Types of Polynomials: Monomial – a #, variable or the product of the two. Binomial – the sum/difference of two monomials. “Bi” means 2  like bicycle, has 2 wheels. example: x2 + 2xy Trinomial – the sum/difference of three monomials. “Tri” means 3  like tricycle, has 3 wheels example: 5a – ab + c4 Polynomials with more than three terms do not have a special name.

Monomial, Binomial, Trinomial? Examples: State whether each expression is a polynomial. If so, identify what type of polynomial. Expression Polynomial? Monomial, Binomial, Trinomial? 1. 2x – 3yz 2. 8n3 + 5n-2 3. -8 4. 6a2 + 3a – a + 11

Polynomial Vocabulary Degree of a monomial – the sum of the exponents of all its variables. Degree of a polynomial – the greatest degree of any one term in the polynomial. (you must find the degree of each term). Standard Form of Polynomials- is ordering terms in descending (decreasing) order by degree.

Finding Degrees of Monomials 5x 8xy 6x3y2 -7y4z 4 11

Polynomial in Standard Form Degrees Polynomial Degree of each term Polynomial in Standard Form Degree of Polynomial 5mn2 -4x2y2 + 3x2 + 5 3a + 7ab – 2a2b + 16 3xy2 – 4x3 + x2y + 6y

Name Using Number of Terms Names Using Degrees Degree Name Using Degree Polynomial Example Number of Terms Name Using Number of Terms Constant 6 Monomial Linear x + 4 Quadratic 4x2 Cubic 4x3 – 2x2 + x

Examples: Put in standard form and find the degree of the polynomial 1. -2xy2z3 2. 3a + 7ab – 2a2b 3. 25 4. h3m + 6h4m2 – 7

Write Polynomials in Order Example 1: Arrange the terms of each polynomial so that the powers of x are in descending order. 3a3x2 – a4 + 4ax5 + 9a2x 2xy3 + y2 + 5x3 – 3x2y

Example 2: Arrange the terms of each polynomial so that the polynomial is in Standard Form. 6x2 + 5 – 8x – 2x3 7x2 + 2x4 – 11

Homework HW Unit 1 Lesson 3 Tell your parents about Academic Night on Thursday! January 31st at 5:15 (Media Center)

Warm Up Jan. 29th 2013 Is this a polynomial? Simplify: (-4m2n3)(3mn4)-1 Simplify: 4x – x + 2x – x Simplify: State the degree. a) 42h3 b) 24x4y2 – x2y5 + x3

Add & Subtract Polynomials Adding Polynomials Hint: combine like terms! Make sure they have the same variable & exponent. (4xy + 7x2 – 6y) + (3xy + 2y – 5x2) We are NOT multiplying or dividing so… DON’T TOUCH THE EXPONENTS!!!!

Example 1: Find the sum of (4x2 + 3x - 7) + (x2 + 10) 2 ways to simplify: Horizontal Vertical (4x2 + 3x – 7) + (x2 + 10) (4x2 + 3x – 7) + ( x2 + 10)

Watch out for mixed up polynomials Watch out for mixed up polynomials! Example 2: Find the sum of (7 + 3x2 + 5xy) + (xy – 2x2 + 2)

Subtracting Polynomials Hint: distribute the subtraction sign and combine like terms! Example 3: Find the difference. (3x2 + 2x – 6) – (2x + x2 + 3)

Example 4: Find the difference. (5ab2 + 3ab) – (2ab2 + 4 – 8ab)

Geometry Application Example 5: Given the perimeter and the measures of 2 sides of a triangle, find the measure of the third side. P = 7x + 3y x – 2y 2x + 3y

Activities! Find a partner and complete the dominoes. After you get them checked by Mrs. Sawyer—start the Polynomial Search. IT IS DUE BEFORE THE END OF CLASS!

Homework HW Unit 1 Lesson 4