Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
Section 5.1.notebook
1
October 18, 2013
Key Words...• polynomial• term• coefficient• degree• constant term• monomial• binomial• trinomial• like terms
Chapter 5 Polynomials
Section 5.1.notebook
2
October 18, 2013
Section 5.1 Modelling Pollynomials
We can use algebra tiles to model an expression...
represents +1
represents 1
Reminder...A +1 tile and a 1 tile represent a zero pair
represents any positive variable (x or n)
represents any negative variable ( x or n)
ex: ex:
Try these...
a) b) c)
d) e)
Section 5.1.notebook
3
October 18, 2013
Modelling, Writing and Classifying Polynomials
For expressions containing terms...we use...
represents
represents
ex: Model
ex: Model
4 positive tiles 3 negative tiles 2 positive tiles
Section 5.1.notebook
4
October 18, 2013
In the term , 3 is the coefficient (number in front of the variable)
In the term , 5 is a constant (value never changes)
In the term , 2 is the coefficient
Polynomial is one term or sum of terms, whose variables have whole number exponents
It has 3 termsNote: Terms are separated by an addition or subtraction sign
is a term
is a term
is a term
has a degree of 2
the term with the greatest exponent determines the degree of the polynomial
has a degree of 2
has a degree of 1
has a degree of 0
Section 5.1.notebook
5
October 18, 2013
Types of Polynomials depend on the number of terms...
Type of Polynomial
Number of Terms Examples Types of tiles
Monomial 12s22n4
has only one type of tile
Binomial 2x2 + 32a 1
2b2 + 3b
has two different types
of tiles
Trinomial 3 c2 + 4c 2x2 + 2x 8
has three different types
of tiles
***Monomials, Binomials and Trinomials are all Polynomials
***Polynomials are written (usually) in descending order (highest exponent to lowest)
ie: 2k 4k2 + 7
written as...
4k2 + 2k + 7
Section 5.1.notebook
6
October 18, 2013
Recognizing the same Polynomials with different variables...
Q: Which of these polynomials can be represented by the same alge tiles? Or which are equivalent?
a) 3x2 5x + 6 b) 5 + 6r + 3r2 c) 5m + 6 + 3m2
3 (x2 tiles) 5 (1 tiles) 5 (m tiles)
5 (x tiles) 6 (r tiles) 6 (+1 tiles)
6 (+1 tiles) 3 (r2 tiles) 3 (m2 tiles)
a and c both use the same kind and # of tiles, therefore they are equivalent
Another method would be to put them in descending order...
a) 3x2 5x + 6 b) 5 + 6r + 3r2 c) 5m + 6 + 3m2
3x2 5x + 6 3r2 + 6r 5 3m2 5m + 6
Same
Textbook: pp. 214 216, #'s 4 16, 18
Section 5.1.notebook
7
October 18, 2013
Grade 9 Math Chapter 5 Section 5.1
Grade:9 Subject:Mathematics
Date:February
Section 5.1.notebook
8
October 18, 2013
1
A
B
C
D
A large white square represents an x2tile, a black rectangle represents a −xtile,anda small white square represents a 1tile.
Write the polynomial represented by this set of algebra tiles.
Section 5.1.notebook
9
October 18, 2013
2
A
B
C
D
A large white square represents an x2tile, a large black square represents a −x2tile, a small white square represents a 1tile, and a small black square represents a −1tile.
How would you model the polynomial with algebra tiles?
Section 5.1.notebook
10
October 18, 2013
3
A
B
C
D
Which of the following expressions are polynomials?
i)
ii)
iii) iv)
i, iii, and iv
ii and iv
i, ii, and iii
i, ii, and iv
Section 5.1.notebook
11
October 18, 2013
4
A
B
C
D
How many terms are in the polynomial ?
10
1
11
3
Section 5.1.notebook
12
October 18, 2013
5
A
B
C
D
Which of the following expressions is a binomial with degree 2?i) ii) iii) iv)
i
ii
iv
iii
Section 5.1.notebook
13
October 18, 2013
6
A
B
C
D
Which of the following expressions are monomials with degree 2?i) ii) iii) iv)
ii and iii
ii and iv
iii and iv
i and ii
Section 5.1.notebook
14
October 18, 2013
7
A
B
C
D
Name the coefficients of the variable in the polynomial
4
4, 10
4, 12
4, 10
Section 5.1.notebook
15
October 18, 2013
8
A
B
C
D
Identify the polynomials that can be represented by the same set of algebra tiles.i) ii) iii) iv)
iii and iv
i and iv
ii and iv
i and ii
Section 5.1.notebook
16
October 18, 2013
9
A
B
C
D
Identify the polynomial that is equivalent to i) ii) iii) iv)
iv
ii
i
iii
Section 5.1.notebook
17
October 18, 2013
10
A
B
C
D
What algebra tiles would you use to model the polynomial ?
6 x2tiles, 4 −xtiles, and 4 1tiles
2 x2tiles, 4 xtiles
4 −x2tiles, 4 xtiles, and 6 1tiles
4 x2tiles, 4 −xtiles, and 6 −1tiles