Introduction to Arithmetic Operations on Polynomials
09/30/2019
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Number Sense Routine
•
Introduction Video
•
Cornell Notes
Topic
-
Arithmetic Operations on
polynomials
E.Q.
- How
do I perform arithmetic
operations on
polynomials?
•
Elbow Partner Activity
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Ticket out the Door
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circle the variable(s) in each
expression:
3x
2
– 2x + 5
7a
x
2
+ 3 + 2y
-
Parts, Operations, & Representations
-
Approximately January 14
th
to February 24
th
This unit will help you develop an
understanding of polynomials, a form of
mathematical expression.
We will learn how to work with:
-
Parts of a Polynomial
-
Polynomial Operations (+)(-)(x)(÷)
-
Representing Polynomials
Polynomial
-
“Poly”
-
many
-
“Nomial”
-
terms
Polynomial
-
A numerical
expression written
with:
-
one term
OR
-
sum/difference of
terms
-
variables that
have whole-
number
exponents
- Polynomial Vocabulary -
-
Variable
-
Any letter that is used to represent
a changing value
(
ex
) 3
x
2
- 2
x
+5
- Polynomial Vocabulary -
-
Coefficient
-
Any number found at the beginning
of a term containing a variable
(
ex
)
3
x
2
-
2
x +5
- Polynomial Vocabulary -
-
Terms
-
Each individual portion of the
expression
-
Can be a number, variable, or the
product of a number & a variable
(
ex
)
3x
2
-
2x
+
5
- Polynomial Vocabulary -
-
Constant
-
Any number by itself, the number
does not change
(
ex
) 3x
2
- 2x +
5
- Polynomial Vocabulary -
-
Degree
-
Refers to how big the exponent is
(
ex
) 3x
2
- 2x +5
- 3x
2
= Degree of 2
- 2x = Degree of 1
- 5 = Degree of 0
Polynomial Example
-
Variables
x
3
, x
2
, -x
-
Coefficients
-6, 4
-
Constants
7
-
# of Terms
4
-6x
3
+ 4x
2
– x + 7
-
Degree (H-L)
Polynomial Example
-
Variables
a
3
, b
2
, c, -x
-
Coefficients
3, -5
-
Constants
-
-
# of Terms
4
3a
3
- 5b
2
+ c - x
-
Degree (H-L)
- Special Case Polynomial Vocabulary -
-
Monomial
-
Polynomial with one term
(
ex
) 2m
(
ex
) 8
(
ex
) n
2
- Special Case Polynomial Vocabulary -
-
Binomial
-
Polynomial with two terms
(
ex
) 3x + 6
(
ex
) 5m
2
– 2m
- Special Case Polynomial Vocabulary -
-
Trinomial
-
Polynomial with three terms
(
ex
) 2x
2
+ 4x + 7
Polynomial Example
Identify each as a monomial, binomial, or
trinomial:
-5x
2
4m
2
+ m + 6
5 x - 3
Guided Practice
http://www.math-
aids.com/cgi/pdf_viewer_2.cgi?script_na
me=pre-
algebra_mono_poly_id_type.pl&case_1=1
&case_2=1&case_3=1&case_4=1&case_
5=1&case_6=1&language=0&memo=&an
swer=1&x=162&y=37
Re-write, then label the following for
each polynomial:
(variable, constant, coefficient)
3x
2
– 2x + 5
7a
x
2
+ 3 + 2y
Algebra Tiles
-
Polynomial
expressions can
be modeled using
algebra tiles
x
2
-x
1
-1
Algebra Tiles
-
Model example
3x
2
– 2x + 5
Algebra Tiles
Who can show how to model:
4m
2
+ m + 6
Algebra Tiles
Who can show how to model:
5m
2
– 2m
Mental Math
Please show with algebra
tiles:
2m
2
+3m – 2
-6m – 2
-2x
2
+4m – 6
10.01.2019
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Number Sense Routine
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Introduction Video
•
Cornell Notes Topic-
Arithmetic Operations on
polynomials E.Q.- How
do I perform arithmetic
operations on
polynomials?
•
Elbow Partner Activity
•
Ticket out the Door
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A) -16
Monomial
B) x – 8
Binomial
C) 4x
Monomial
D) 2x
2
– 8x + 3
Trinomial
E) -5x + 5
Binomial
F) 5x
2
Monomial
G) -2x
2
+ 2x – 3
Trinomial
H) -3x
2
+ 8
Binomial
Please show with algebra
tiles:
5m
2
+2m – 8
-2m – 9
-3x
2
+7m + 5
In each polynomial, identify which terms
have the same variable, then identify
which terms have the same degree
(exponent).
7a + 3b
2
-2a + 5 -b
2
+ 0
-9x
2
+7m + x
2
- 2 + 1m – 2k
Simplifying
-
Like terms
can be simplified in a
polynomial
-
Likes Terms have:
-
The same
variable
-
The same
degree
(
ex
)
x
2
and 2x
2
are like terms
x
2
-3 - x
2
- 2x + 2 + x
2
- x + x
Simplify the following polynomials by
grouping like terms together, remember to
represent it from Highest Degree to
Lowest Degree:
7a + 3b
2
-2a + 5 -b
2
+ 0
-9x
2
+7m + x
2
- 2 + 1m – 2k
Polynomial Operations
- Addition & Subtraction -
-
When adding two or more polynomials
together, each polynomial is
sectioned
off with brackets
(
ex
) 7s + 14 added to –6s
2
+ 2 – 6
is written as
(7s + 14) + (-6s
2
+ 2 – 6 )
Polynomial Operations
- Addition & Subtraction -
-
Drop the brackets &
combine like terms
-
You should order your terms from
highest degree to lowest degree
(
ex
) (7s + 14) + (-6s
2
+ 2 – 6 )
Polynomial Operations
- Addition & Subtraction -
Addition Practice One
(3x
2
+ 6) + (4x
2
– 8)
Polynomial Operations
- Addition & Subtraction -
Addition Practice Two
Find the perimeter
of the following shape.
3x + 2
2x + 1
Polynomial Operations
- Addition & Subtraction -
-
When subtracting, it is important to
remember your
integer rules
(
ex
) 2 – (5) = 2 + (-5) = -3
Polynomial Operations
- Addition & Subtraction -
-
When subtracting, it is important to
remember your
integer rules
(
ex
) 4 – (-3) = 4 + 3 = 7
Polynomial Operations
- Addition & Subtraction -
-
When subtracting, it is important to
remember your
integer rules
(
ex
) 5 – (8-2) = 5 – 8 + 2 = -3 + 2 = -1
Check:
5 – (8-2) = 5 – (6) = 5 + (-6) = -1
Polynomial Operations
- Addition & Subtraction -
Remember all of the positives (+) being
subtracted change to negatives (-) and
all the negatives (-) being subtracted
change to positives (+)
Find the perimeter of the following shape.
Please show ALL your steps.
3x + 2
2x + 1
2x + 1
1x + 6
x
1x + 6
x + 7
Polynomial Operations
- Addition & Subtraction -
Subtraction Integer Rule Practice One
-(2x+6) =
-2x - 6
Polynomial Operations
- Addition & Subtraction -
Subtraction Integer Rule Practice One
-(3x+1) =
-3x - 1
Polynomial Operations
- Addition & Subtraction -
Subtraction Integer Rule Practice One
-(-4a
2
+2ab + 5b -9) =
4a
2
- 2ab - 5b +9
Polynomial Operations
- Addition & Subtraction -
-
Like addition, drop brackets and group
like terms
(
ex
) (-2a
2
+ a -1) – (a
2
- 3a + 2)
-2a
2
+ a -1 - a
2
+ 3a – 2
-2a
2
- a
2
+ a + 3a – 1 – 2
-3a
2
+ 4a - 3
Polynomial Operations
- Addition & Subtraction -
Addition Practice One
(4m
2
+ 4m -5) + (2m
2
– 2m + 1)
10.02.2019
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Number Sense Routine
•
Introduction Video
•
Cornell Notes
Topic
-
Arithmetic Operations on
polynomials
E.Q.
- How do
I perform arithmetic
operations on
polynomials?
•
Elbow Partner Activity
•
Ticket out the Door
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Complete the following addition and
subtraction problems, please show ALL of
your steps:
(2x
2
- 4y + 2y
2
) - (8x
2
- 5y + 7y
2
)
(6a
2
- 7ab + 12b
2
) + (13a
2
) + (5ab + 2b
2
)
Polynomial Operations
- Addition & Subtraction -
Addition Practice
(4m
2
+ 4m -5) + (2m
2
– 2m + 1)
Polynomial Operations
- Addition & Subtraction -
Subtraction Practice
(1- 3r + r
2
) - (4r + 5 – 3r
2
)
Textbook Questions
Addition
Pg 228-229
Qs 3, 6, 8(a,c,e,g), 10(i, iii), 15(a,b)
Subtraction
Pg 235-236
Qs 7(a,b), 8(a,c,e,g), 13(a,b), 15(a,b)
Complete the following addition and
subtraction problems, please show ALL of
your steps:
(2k
2
- 3k + 2) + (-3k
2
- 3k + 2)
(3x
2
- 2x + 3) - (2x
2
+ 4)
Complete the following addition and
subtraction problems,
using algebra tiles
:
(7k
2
+ 2k - 9) + (-5k + 2)
(7x
2
+ 8x + 1) - (6x
2
- 4)
Polynomial Operations
- Multiplication & Division by a Constant-
https://www.youtube.com/watch?feature
=player_embedded&v=ZObKgGXrGy4
Polynomial Operations
- Multiplication & Division by a Constant -
2(-3m² + 5m – 4)
Polynomial Operations
- Multiplication & Division by a Constant -
-4(3n² - n + 5)
Polynomial Operations
- Multiplication & Division by a Constant -
(9z + 6) ÷ 3
Polynomial Operations
- Multiplication & Division by a Constant -
(8x + 12) ÷ (-4)
Determine each product or quotient,
please
show all of your work
:
(-2gh + 6h
2
– 3g
2
– 9g)(3)
(12t
2
– 24ut – 48t) ÷ (-6)
10.03.2019
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Number Sense Routine
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Cornell Notes Multiplying
and dividing polynomials
continuation
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Group Activity
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Student/teacher Dialog
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5.A. Which of these products is modelled
by the algebra tiles below?
i)
2(-2n
2
+ 3n + 4)
ii)
2(2n
2
– 3n + 4)
iii)
-2(2n
2
– 3n + 4)
14. Here is a student’s solution for this
question: (-14m
2
– 28m + 7) ÷ (-7). Is
this model correct?
(-14m
2
– 28m + 7) ÷ (-7)
=
-14m
2
+
-28m
+
-7
-7 7 7
= 2m
2
- 4m + 0
= -2m
Polynomial Operations
- Multiplication & Division by a Monomial -
-
It is important to remember your Power
Laws!
-
Multiplying
-
If the variables are the same,
add the
exponents
(
ex
) (x
3
)(x
4
) = x
(5+4)
Polynomial Operations
- Multiplication & Division by a Monomial -
(x
2
)(x
3
) =
(m
6
)(m
3
) =
Polynomial Operations
- Multiplication & Division by a Monomial -
-
Multiplying
-
If the variables are different, we write
them
side-by-side
meaning that we
are multiplying them
-
Any
coefficients get multiplied as
normal
(
ex
) (3x)(2y) = 6xy
Polynomial Operations
- Multiplication & Division by a Monomial -
2z(3z + 4)
**Remember your distributive property
Polynomial Operations
- Multiplication & Division by a Monomial -
-2x(-5x + 3)
**Remember your distributive property
Polynomial Operations
- Multiplication & Division by a Monomial -
-
It is important to remember your Power
Laws!
-
Dividing
-
If the variables are the same,
subtract
the exponents
(
ex
) (x
7
)÷(x
3
) = x
(7-3)
Polynomial Operations
- Multiplication & Division by a Monomial -
12x
2x
Polynomial Operations
- Multiplication & Division by a Monomial -
30k
2
– 18k
-6k
Determine each product or quotient,
please
show all of your work
:
(-2gh + 6h
2
– 3g
2
– 9g)(3g)
(40rs- 35r) ÷ (-5r)
(14n
2
+ 42np) ÷ (-7n)
This unit focuses on developing an understanding of polynomials in mathematical expressions. You will learn about the parts of a polynomial, polynomial operations, and representing polynomials. The topics cover performing arithmetic operations on polynomials, identifying variables in expressions, learning about polynomial vocabulary such as variables and coefficients, and more.
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Presentation Transcript
09/30/2019 Number Sense Routine Simplest form: Agenda Number Sense Routine Introduction Video Cornell Notes Topic- Arithmetic Operations on polynomials E.Q.- How do I perform arithmetic operations on polynomials? Elbow Partner Activity Ticket out the Door 12 15 15 24 21 54
Mental Math Mental Math Mental Math Mental Math circle the variable(s) in each expression: 3x2 2x + 5 7a x2+ 3 + 2y
Polynomials Polynomials Polynomials Polynomials - Parts, Operations, & Representations Parts, Operations, & Representations - Approximately January 14th to February 24th
Intro Intro Intro Intro This unit will help you develop an understanding of polynomials, a form of mathematical expression. We will learn how to work with: - Parts of a Polynomial - Polynomial Operations (+)(-)(x)( ) - Representing Polynomials
Polynomials Polynomials Polynomials Polynomials Polynomial Polynomial http://t3.gstatic.com/images?q=tbn:ANd9GcTsAz03eV0C328qAX4gqywG9XqSq-TCPj9eolGicS6awE4O8DQW - Poly -many many - Nomial -terms terms
Polynomials Polynomials Polynomials Polynomials Polynomial Polynomial http://t3.gstatic.com/images?q=tbn:ANd9GcTsAz03eV0C328qAX4gqywG9XqSq-TCPj9eolGicS6awE4O8DQW - A numerical expression written with: -one term one term OR -sum/difference of sum/difference of terms terms -variables that variables that have whole have whole- - number number exponents exponents
Polynomials Polynomials Polynomials Polynomials - - Polynomial Vocabulary Polynomial Vocabulary - - - Variable Variable -Any letter that is used to represent a changing value (ex) 3x x2 - 2x x +5
Polynomials Polynomials Polynomials Polynomials - - Polynomial Vocabulary Polynomial Vocabulary - - - Coefficient Coefficient -Any number found at the beginning of a term containing a variable (ex) 3 3x2 - 2 2x +5
Polynomials Polynomials Polynomials Polynomials - - Polynomial Vocabulary Polynomial Vocabulary - - - Terms Terms -Each individual portion of the expression - Can be a number, variable, or the product of a number & a variable (ex) 3x2 - 2x +5
Polynomials Polynomials Polynomials Polynomials - - Polynomial Vocabulary Polynomial Vocabulary - - - Constant Constant -Any number by itself, the number does not change (ex) 3x2 - 2x +5 5
Polynomials Polynomials Polynomials Polynomials - - Polynomial Vocabulary Polynomial Vocabulary - - - Degree Degree -Refers to how big the exponent is (ex) 3x2 - 2x +5 - 3x2 = Degree of 2 - 2x = Degree of 1 - 5 = Degree of 0
Polynomials Polynomials Polynomials Polynomials Polynomial Example Polynomial Example - Variables x3, x2, -x - Coefficients -6, 4 - Constants 7 - # of Terms 4 - -6x 6x3 3 + 4x + 4x2 2 x + 7 x + 7 - Degree (H-L)
Polynomials Polynomials Polynomials Polynomials Polynomial Example Polynomial Example - Variables a3, b2, c, -x - Coefficients 3, -5 - Constants - - # of Terms 4 3a 3a3 3 - - 5b 5b2 2 + c + c - - x x - Degree (H-L)
Polynomials Polynomials Polynomials Polynomials - - Special Case Polynomial Vocabulary Special Case Polynomial Vocabulary - - - Monomial Monomial -Polynomial with one term (ex) 2m (ex) 8 (ex) n2
Polynomials Polynomials Polynomials Polynomials - - Special Case Polynomial Vocabulary Special Case Polynomial Vocabulary - - - Binomial Binomial -Polynomial with two terms (ex) 3x + 6 (ex) 5m2 2m
Polynomials Polynomials Polynomials Polynomials - - Special Case Polynomial Vocabulary Special Case Polynomial Vocabulary - - - Trinomial Trinomial -Polynomial with three terms (ex) 2x2 + 4x + 7
Polynomials Polynomials Polynomials Polynomials Polynomial Example Polynomial Example Identify each as a monomial, binomial, or trinomial: -5x2 4m2 + m + 6 5 x - 3
Polynomials Polynomials Polynomials Polynomials Guided Practice Guided Practice http://www.math- aids.com/cgi/pdf_viewer_2.cgi?script_na me=pre- algebra_mono_poly_id_type.pl&case_1=1 &case_2=1&case_3=1&case_4=1&case_ 5=1&case_6=1&language=0&memo=&an swer=1&x=162&y=37
Mental Math Mental Math Mental Math Mental Math Re-write, then label the following for each polynomial: (variable, constant, coefficient) 3x2 2x + 5 7a x2 + 3 + 2y
Polynomials Polynomials Polynomials Polynomials 1 1 Algebra Tiles Algebra Tiles x x2 2 x x - Polynomial expressions can be modeled using algebra tiles - -1 1 - -x x - -x x2 2
Polynomials Polynomials Polynomials Polynomials Algebra Tiles Algebra Tiles - Model example 3x2 2x + 5 x x2 2 - -x x - -x x x x2 2 x x2 2
Polynomials Polynomials Polynomials Polynomials Algebra Tiles Algebra Tiles Who can show how to model: 4m2 + m + 6
Polynomials Polynomials Polynomials Polynomials Algebra Tiles Algebra Tiles Who can show how to model: 5m2 2m
Polynomials Polynomials Polynomials Polynomials Mental Math Mental Math Please show with algebra tiles: 2m2 +3m 2 -6m 2 -2x2 +4m 6
10.01.2019 Agenda Number Sense Routine Introduction Video Cornell Notes Topic- Arithmetic Operations on polynomials E.Q.- How do I perform arithmetic operations on polynomials? Elbow Partner Activity Ticket out the Door Number Sense Routine Simplest form: 18 20 6 16 35 45
Polynomials Polynomials Polynomials Polynomials A) A) - -16 B) x B) x 8 8 C) 4x C) 4x D) 2x D) 2x2 2 8x + 3 E) E) - -5x + 5 5x + 5 F) 5x F) 5x2 2 G) G) - -2x 2x2 H) H) - -3x 3x2 16 Monomial Monomial Binomial Binomial Monomial Monomial Trinomial Trinomial Binomial Binomial Monomial Monomial Trinomial Trinomial Binomial Binomial 8x + 3 2 + 2x + 2x 3 3 + 8 2 + 8
Mental Math Mental Math Mental Math Mental Math Please show with algebra tiles: 5m2 +2m 8 -2m 9 -3x2 +7m + 5
Mental Math Mental Math Mental Math Mental Math In each polynomial, identify which terms have the same variable, then identify which terms have the same degree (exponent). 7a + 3b2 -2a + 5 -b2 + 0 -9x2 +7m + x2 - 2 + 1m 2k
Polynomials Polynomials Polynomials Polynomials Simplifying Simplifying - Like terms Like terms can be simplified in a polynomial -Likes Terms have: -The same variable variable -The same degree degree (ex ex) x2 and 2x2 are like terms x2 -3 - x2 - 2x + 2 + x2 - x + x
Mental Math Mental Math Mental Math Mental Math Simplify the following polynomials by grouping like terms together, remember to represent it from Highest Degree to Lowest Degree: 7a + 3b2 -2a + 5 -b2 + 0 -9x2 +7m + x2 - 2 + 1m 2k
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - - When adding two or more polynomials together, each polynomial is sectioned off with brackets off with brackets sectioned (ex ex) 7s + 14 added to 6s2 + 2 6 is written as (7s + 14) + (-6s2 + 2 6 )
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - - Drop the brackets & combine like terms combine like terms - You should order your terms from highest degree to lowest degree highest degree to lowest degree (ex ex) (7s + 14) + (-6s2 + 2 6 )
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Addition Practice One Addition Practice One (3x2 + 6) + (4x2 8)
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Addition Practice Two Addition Practice Two 3x + 2 Find the perimeter of the following shape. 2x + 1
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - - When subtracting, it is important to remember your integer rules integer rules (ex ex) 2 (5) = 2 + (-5) = -3
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - - When subtracting, it is important to remember your integer rules integer rules (ex ex) 4 (-3) = 4 + 3 = 7
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - - When subtracting, it is important to remember your integer rules integer rules (ex ex) 5 (8-2) = 5 8 + 2 = -3 + 2 = -1 Check: 5 (8-2) = 5 (6) = 5 + (-6) = -1
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Remember all of the positives (+) being subtracted change to negatives (-) and all the negatives (-) being subtracted change to positives (+)
Mental Math Mental Math Mental Math Mental Math Find the perimeter of the following shape. Please show ALL your steps. 1x + 6 x + 7 1x + 6 x 2x + 1 2x + 1 3x + 2
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Subtraction Integer Rule Practice One Subtraction Integer Rule Practice One -(2x+6) = -2x - 6
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Subtraction Integer Rule Practice One Subtraction Integer Rule Practice One -(3x+1) = -3x - 1
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Subtraction Integer Rule Practice One Subtraction Integer Rule Practice One -(-4a2+2ab + 5b -9) = 4a2 - 2ab - 5b +9
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - - Like addition, drop brackets and group like terms (ex ex) (-2a2 + a -1) (a2 - 3a + 2) -2a2 + a -1 - a2 + 3a 2 -2a2 - a2 + a + 3a 1 2 -3a2 + 4a - 3
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Addition Practice One Addition Practice One (4m2 + 4m -5) + (2m2 2m + 1)
10.02.2019 Agenda Number Sense Routine Introduction Video Cornell Notes Topic- Arithmetic Operations on polynomials E.Q.- How do I perform arithmetic operations on polynomials? Elbow Partner Activity Ticket out the Door Number Sense Routine Simplest form: Simplest form: 16 62 16 62 15 20 32 24 15 20 32 24
Mental Math Mental Math Mental Math Mental Math Complete the following addition and subtraction problems, please show ALL of your steps: (2x2- 4y + 2y2) - (8x2- 5y + 7y2) (6a2- 7ab + 12b2) + (13a2) + (5ab + 2b2)
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Addition Practice Addition Practice (4m2 + 4m -5) + (2m2 2m + 1)
Polynomials Polynomials Polynomials Polynomials Polynomial Operations Polynomial Operations - - Addition & Subtraction Addition & Subtraction - - Subtraction Practice Subtraction Practice (1- 3r + r2) - (4r + 5 3r2)
Polynomials Polynomials Polynomials Polynomials Textbook Questions Textbook Questions Addition Addition Pg 228-229 Qs 3, 6, 8(a,c,e,g), 10(i, iii), 15(a,b) Subtraction Subtraction Pg 235-236 Qs 7(a,b), 8(a,c,e,g), 13(a,b), 15(a,b)
Mental Math Mental Math Mental Math Mental Math Complete the following addition and subtraction problems, please show ALL of your steps: (2k2- 3k + 2) + (-3k2- 3k + 2) (3x2- 2x + 3) - (2x2 + 4)
