Algebra Day 1

Learning Goal I can identify the parts of a polynomial I can identify like terms

Minds ON You've just got a part-time job bagging groceries at the local store. Customers are fussy about which bag their purchases go into. Discuss with a partner some of the “rules” for bagging groceries.

One rule of thumb is to "put the apples with the apples, and the oranges with the oranges." You may not know it, but you've already learned a basic rule about working with polynomials! Polynomials?!! What do they have to do with bagging groceries? All you know is you shouldn't put heavy things on top of the eggs in the same bag

Turn and Talk What does it mean to simplify? Can you give an example?

Definitions Terms of an expression – in an algebraic expression, parts that are separated by + and – signs are the terms eg. 3x2 , -5x , 4 Like terms – have the same variables and exponents; can be combined by addition or subtraction Eg. 3x and 5x (3x + 5x = 8x) 6x2 and -10x2 (6x2 -10x2 = -4x2 )   Unlike terms – have different variables and/or exponents and cannot be combined by addition or subtraction Eg. 3x and 4y or 6x2 and 3x Variable term – a term that contains a variable eg. 3x2, -5x   Constant term – a term that does not have a variable, but only contains a number, eg. 4 Coefficient – in a term, the numerical part is called the coefficient eg. In 3x, the 3 Variable – the part of the term with a non-number eg. In the 3x, the x

Types of Polynomials Polynomials – algebraic expressions where terms are added and subtracted eg. 3x2 – 5x + 4 Monomials - a polynomial with one term eg. 3x2   Binomial – a polynomial with two terms eg. 3x2 + 4 Trinomial – a polynomial with three terms eg. 4x2 - 2x + 1

Simplifying a polynomial – when you add and subtract like terms

Explanation of terminology In integers, how did you do - 8 – 7? How do you say this? “negative 8 and negative 7” (addition of 2 negatives) “negative 8 subtract 7” (add the opposite) They are all “+”, but when the negative sign goes with a”+”, it changes to a negative we simplify like we did for: (-8) + (-7) +(-6) + (-2) – (-4) ]

Examples Determine the type of polynomial given: a. 2x – 2x2 b. 5x + 4y + 6z c. 3

Simplify each polynomial 3x + 5x b. 6y – 8y c. 6p – 2p +10p d. 3m + 4n – 8m + 2n e. –x3 + x2 + 2x3 – x +3x2

More Examples What could the question be if the answer is 3a – 2b 7a2

What could this expression represent?

Homework Pg. 257 #