Introduction to Polynomials.pptx

09/30/2019
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:
12
15
15
24
21
54

circle the variable(s) in each
expression:
3x2 – 2x + 5
7a
x2 + 3 + 2y

- Parts, Operations, & Representations -
Approximately January 14th to February 24th

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) 3x2 - 2x +5

- Coefficient
-Any number found at the beginning
of a term containing a variable
(ex) 3x2 - 2x +5

- Terms
-Each individual portion of the
expression
- Can be a number, variable, or the
product of a number & a variable
(ex) 3x2 - 2x +5

- Constant
-Any number by itself, the number
does not change
(ex) 3x2 - 2x +5

- Degree
-Refers to how big the exponent is
(ex) 3x2 - 2x +5
- 3x2 = Degree of 2
- 2x = Degree of 1
- 5 = Degree of 0

Polynomial Example
- Variables
x3, x2, -x
- Coefficients
-6, 4
- Constants
7
- # of Terms
4
-6x3 + 4x2 – x + 7
- Degree (H-L)

Polynomial Example
- Variables
a3, b2, c, -x
- Coefficients
3, -5
- Constants
-
- # of Terms
4
3a3 - 5b2 + c - x
- Degree (H-L)

- Special Case Polynomial Vocabulary -
- Monomial
-Polynomial with one term
(ex) 2m
(ex) 8
(ex) n2

- Binomial
-Polynomial with two terms
(ex) 3x + 6
(ex) 5m2 – 2m

- Trinomial
-Polynomial with three terms
(ex) 2x2 + 4x + 7

Polynomial Example
Identify each as a monomial, binomial, or
trinomial:
-5x2
4m2 + 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)
3x2 – 2x + 5
7a
x2 + 3 + 2y

Algebra Tiles
- Polynomial
expressions can
be modeled using
algebra tiles
x2
-x2
x
-x
1
-1

Algebra Tiles
- Model example
3x2 – 2x + 5
x2 -x
x2 x2 -x

Algebra Tiles
Who can show how to model:
4m2 + m + 6

Algebra Tiles
Who can show how to model:
5m2 – 2m

Mental Math
Please show with algebra
tiles:
2m2 +3m – 2
-6m – 2
-2x2 +4m – 6

10.01.2019
Agenda
polynomials E.Q.- How
do I perform arithmetic
operations on
polynomials?
• Simplest form:
18
20
6
16
35
45

A) -16 Monomial
B) x – 8 Binomial
C) 4x Monomial
D) 2x2 – 8x + 3 Trinomial
E) -5x + 5 Binomial
F) 5x2 Monomial
G) -2x2 + 2x – 3 Trinomial
H) -3x2 + 8 Binomial

Please show with algebra
tiles:
5m2 +2m – 8
-2m – 9
-3x2 +7m + 5

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

Simplifying
- Like terms can be simplified in a
polynomial
- Likes Terms have:
-The same variable
-The same degree
(ex) x2 and 2x2 are like terms
x2 -3 - x2 - 2x + 2 + x2 - x + x

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

Polynomial Operations
- Addition & Subtraction -
- When adding two or more polynomials
together, each polynomial is sectioned
off with brackets
(ex) 7s + 14 added to –6s2 + 2 – 6
is written as
(7s + 14) + (-6s2 + 2 – 6 )

- Drop the brackets & combine like terms
- You should order your terms from
highest degree to lowest degree
(ex) (7s + 14) + (-6s2 + 2 – 6 )

Addition Practice One
(3x2 + 6) + (4x2 – 8)

Addition Practice Two
Find the perimeter
of the following shape.
3x + 2
2x + 1

- When subtracting, it is important to
remember your integer rules
(ex) 2 – (5) = 2 + (-5) = -3

(ex) 4 – (-3) = 4 + 3 = 7

(ex) 5 – (8-2) = 5 – 8 + 2 = -3 + 2 = -1
Check:
5 – (8-2) = 5 – (6) = 5 + (-6) = -1

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

Subtraction Integer Rule Practice One
-(2x+6) =
-2x - 6

-(3x+1) =
-3x - 1

-(-4a2+2ab + 5b -9) =
4a2 - 2ab - 5b +9

- Like addition, drop brackets and group
like terms
(ex) (-2a2 + a -1) – (a2 - 3a + 2)
-2a2 + a -1 - a2 + 3a – 2
-2a2 - a2 + a + 3a – 1 – 2
-3a2 + 4a - 3

Addition Practice One
(4m2 + 4m -5) + (2m2 – 2m + 1)

10.02.2019
Agenda
polynomials E.Q.- How do
I perform arithmetic
operations on
polynomials?
• Simplest form:
•
16
62
15
20
32
24
Simplest form:
16
62
15
20
32
24

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)

Addition Practice
(4m2 + 4m -5) + (2m2 – 2m + 1)

Subtraction Practice
(1- 3r + r2) - (4r + 5 – 3r2)

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)

subtraction problems, please show ALL of
your steps:
(2k2- 3k + 2) + (-3k2- 3k + 2)
(3x2- 2x + 3) - (2x2 + 4)

subtraction problems, using algebra tiles:
(7k2+ 2k - 9) + (-5k + 2)
(7x2 + 8x + 1) - (6x2 - 4)

- Multiplication & Division by a Constant-
https://www.youtube.com/watch?feature
=player_embedded&v=ZObKgGXrGy4

- Multiplication & Division by a Constant -
2(-3m² + 5m – 4)

-4(3n² - n + 5)

(9z + 6) ÷ 3

(8x + 12) ÷ (-4)

4𝑠2
− 8
4

−3𝑚2
+ 15𝑚𝑛 − 21𝑛2
−3

Determine each product or quotient,
please show all of your work:
(-2gh + 6h2 – 3g2 – 9g)(3)
(12t2 – 24ut – 48t) ÷ (-6)

10.03.2019
Agenda
• Cornell Notes Multiplying
and dividing polynomials
continuation
• Group Activity
• Student/teacher Dialog
Make X the Subject
7
𝑥
𝑋
3
63
5
𝑥
𝑋
4
100
4
𝑥
𝑋
2
40
Simplest form:
16
62
15
20
32
24
Make X the Subject
7
𝑥
𝑋
3
63
5
𝑥
𝑋
4
100
4
𝑥
𝑋
2
40

5.A. Which of these products is modelled
by the algebra tiles below?
i) 2(-2n2 + 3n + 4)
ii) 2(2n2 – 3n + 4)
iii) -2(2n2 – 3n + 4)

14. Here is a student’s solution for this
question: (-14m2 – 28m + 7) ÷ (-7). Is
this model correct?
(-14m2 – 28m + 7) ÷ (-7)
= -14m2 + -28m + -7
-7 7 7
= 2m2 - 4m + 0
= -2m

- Multiplication & Division by a Monomial -
- It is important to remember your Power
Laws!
- Multiplying
- If the variables are the same, add the
exponents
(ex) (x3 )(x4) = x(5+4)

(x2 )(x3) =
(m6)(m3) =

- 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

2z(3z + 4)
**Remember your distributive property

-2x(-5x + 3)
**Remember your distributive property

- It is important to remember your Power
Laws!
- Dividing
-If the variables are the same, subtract
the exponents
(ex) (x7)÷(x3) = x(7-3)

12x
2x

30k2 – 18k
-6k

Determine each product or quotient,
please show all of your work:
(-2gh + 6h2 – 3g2 – 9g)(3g)
(40rs- 35r) ÷ (-5r)
(14n2 + 42np) ÷ (-7n)

Introduction to Polynomials.pptx

Recommended

Recommended

More Related Content

Similar to Introduction to Polynomials.pptx

Similar to Introduction to Polynomials.pptx (20)

Recently uploaded

Recently uploaded (20)

Introduction to Polynomials.pptx