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
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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 )
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Unlike terms – have different
variables and/or exponents and
cannot be combined by addition or
subtraction
Eg. 3x and 4y or 6x2 and 3x
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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
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• Binomial – a polynomial
with two terms eg. 3x2 + 4
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• 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?
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“negative 8 and negative 7” (addition of 2
negatives)
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“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
a. 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
a. 3a – 2b
b. 7a2
What could this expression represent?
• 2x + 5
Homework
• Pg. 257 #