warm upjan. 28 th 1. 2. 3. 4. 5.. polynomials a polynomial is a monomial or a sum of monomials...

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

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Warm Up Jan. 28th 1.

Polynomials

A polynomial is a monomial or a sum of monomials

Example: x3 + xy + y2

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 wheelsexample: 5a – ab + c4

Polynomials with more than three terms do not have a special name.

Classifying Polynomials

Page 4: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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

Page 5: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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.

Page 6: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Finding Degrees of Monomials

1. 5x

2. 6x3y2

3. 4

4. 8xy

5. -7y4z

6. 11

Page 7: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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

Page 8: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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

Page 9: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Examples: Put in standard form and find the degree of the polynomial

1. -2xy2z3 2. 3a + 7ab – 2a2b

3. 25 4. h3m + 6h4m2 – 7

Page 10: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Example 1: Arrange the terms of each polynomial so that the powers of x are in descending order.

1. 3a3x2 – a4 + 4ax5 + 9a2x

2. 2xy3 + y2 + 5x3 – 3x2y

Write Polynomials in Order

Page 11: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Example 2: Arrange the terms of each polynomial so that the polynomial is in Standard Form.

1. 6x2 + 5 – 8x – 2x3

2. 7x2 + 2x4 – 11

Page 12: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

HomeworkHW Unit 1 Lesson 3

Tell your parents about Academic Night on Thursday!

January 31st at 5:15 (Media Center)

Page 13: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Warm Up Jan. 29th 20131. Is this a polynomial?

2. Simplify: (-4m2n3)(3mn4)-1

3. Simplify: 4x – x + 2x – x

4. Simplify:

5. State the degree.a) 42h3 b) 24x4y2 – x2y5 + x3

53 2

Page 14: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Add & Subtract PolynomialsAdding 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!!!!

Page 15: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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)

Page 16: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Watch out for mixed up polynomials!

Example 2: Find the sum of(7 + 3x2 + 5xy) + (xy – 2x2 + 2)

Page 17: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Subtracting Polynomials

Hint: distribute the subtraction sign and combine like terms!

Example 3: Find the difference.(3x2 + 2x – 6) – (2x + x2 + 3)

Page 18: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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

Page 19: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

Geometry ApplicationExample 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

Page 20: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

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!

Page 21: Warm UpJan. 28 th 1. 2. 3. 4. 5.. Polynomials A polynomial is a monomial or a sum of monomials Example: x 3 + xy + y 2

HomeworkHW Unit 1 Lesson 4

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