Combine Like Terms 3x – 6 + 2x – 8 3x – 7 + 12x + 10 Warm-up Combine Like Terms 3x – 6 + 2x – 8 3x – 7 + 12x + 10 10xy + 5y – 6xy – 14y 5x – 14 15x + 3 4xy – 9y

Sum and Product Puzzles 1. 2. 3. 56 30 9 -3 -3 4 14 3 10 -6 18 13 Find two numbers that multiply to get the top number and add together to get the bottom number.

How do we name, add, and subtract polynomials? Math I UNIT QUESTION: In what ways can algebraic methods be used in problems solving? Standard: MM1A2 Today’s Question: How do we name, add, and subtract polynomials? Standard: MM1A2c

Adding and Subtracting Polynomials MONOMIALS: A monomial is _______________ ____________________________ ______________________  Some examples of monomials are: a number, variable, or a product of numbers and variables. x -20 4y -3a5

POLYNOMIALS:  A polynomial is the ___________ or _________ of monomials. monomial the sum  An example of a polynomial in one variable, x, would be x3 + 6x2 + 12x + 8  How many MONOMIALS are there in the above polynomial? 4

 The largest exponent in the polynomial determines the DEGREE OF A POLYNOMIAL.  Example: The degree of 9 – 7x – 4x2 is ____ because ____the largest exponent in the polynomial. 2 2 Example: Find the degree of the following polynomial: x4 + 6x3 + 7x5 + 12x 5

STANDARD FORM  The terms of a polynomial are in STANDARD FORM if they are ordered from left to right in ______________ order; which means from the LARGEST exponent to the smallest. decreasing  The coefficient of the first term is called the ______________________. leading coefficient Example – Write this in standard form: x4 + 6x3 + 7x5 + 12x What is the leading coefficient?

decreasing – 4x3 + x + 9 – 5x3 + 3x2 + 4x - 2 STANDARD FORM  To write a polynomial in Standard Form, arrange the terms of the polynomial in ______________ order according to the exponent of the variables. decreasing  Example: Write 9 + x – 4x3 in standard form. – 4x3 + x + 9  Example: Write 3x2 – 2 + 4x – 5x3 in standard form. – 5x3 + 3x2 + 4x - 2

In your own notes:

Some polynomials have SPECIAL NAMES that are determined by the following: Their __________ or Their __________ of terms Draw the following Charts in YOUR notes. degree number

# of Terms Name by # of Terms Monomial 2 Binomial 3 Trinomial 4+ Polynomial

Degree Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic (largest exponent) Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic

Now, back to the WS

12 8x 4x2 + 3 5x3 + x2 3x2 – 4x + 6 Polynomial Name by # of Terms DEGREE Name by Degree 12 8x 4x2 + 3 5x3 + x2 3x2 – 4x + 6 Monomial 0 Constant 1 Monomial 1 Linear Binomial 2 Quadratic 2 Binomial 3 Cubic 3 Trinomial 2 Quadratic

Now, a few examples to add to YOUR notes:

Special Names: Degree Name: # of Terms Name: Linear Binomial

Special Names: Degree Name: # of Terms Name: Cubic Monomial

Special Names: Degree Name: # of Terms Name: Quadratic Binomial

Special Names: Degree Name: # of Terms Name: Cubic Trinomial

Adding Polynomials Back to your WS

drop the parenthesis and combine like terms  When adding polynomials _________________________________________________________ drop the parenthesis and combine like terms

Example 5a2 – 2b2

1. 3x2 + x + 2

2. x2 + 2x – 2

3. -2x2 + 3x – 5

4. -x + 6

Back to your notes When SUBTRACTING polynomials Drop the 1st parenthesis then distribute the NEGATIVE to the 2nd parenthesis.

3a2 + 10a – 8a2 + a – 5a2 + 11a

7x – 3 – 9x + 2 – 2x – 1

3x2 + 2x – 4 – 2x2 – x + 1 x2 + x – 3

Class Work Red Workbook p. 61 Lesson Practice 2.1 #16 – 23

Home Work Textbook p. 61 #1 – 14