-6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2...
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Transcript of -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2...
![Page 1: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/1.jpg)
-6a – 13a = -19a
-8n + 14n = 6n
10r - 19r = -9r
![Page 2: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/2.jpg)
5xy + 3xy = 8xy
2s2
10ac + 19ac = 9ac
9s2 + 11s2 =
![Page 3: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/3.jpg)
2n x 8 = 16n
24a2
5e x 9e = 45e2
6a x 4a =
![Page 4: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/4.jpg)
28b ÷ 7 = 4b
52
24 ÷ 4d = 6/d
53 ÷ 5 =
![Page 5: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/5.jpg)
x - 3.5 = 8.9 – 3x
4x = 12.4
x+ -3.5 = 8.93x4x = 8.9 + 3.5
x = 3.1
![Page 6: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/6.jpg)
2x + 20 = 12
X =
2x = -8
-4
![Page 7: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/7.jpg)
2/5 = 4y + 16 2/5
= y
= 4y-16
-4
![Page 8: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/8.jpg)
24 + 4c = -2c
= -24
4c = -2c -
c =
24
6c
-4
![Page 9: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/9.jpg)
12123 = ____10
22 = ______2
50
10110
![Page 10: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/10.jpg)
4 2 4 4 1256
6 8 - 10
=4 2 =4 4 =
1
= 62=
6 10
6 8
= 36
![Page 11: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/11.jpg)
Rename 2.025 as a mixed number
Let x = .025 (x) = (.025)
10x = 0.25
10 10
(10x) = (0.25)100 100
1000x = 25.25
![Page 12: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/12.jpg)
Rename 2.025 as a mixed number
10x = .25 1000x = 25.25
=990x 25
x = 25/900 or 1/ 36
![Page 13: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/13.jpg)
Rename 2.025 as a mixed number
x = 25/900 or 1/ 36
2.025 = 2 + .025
.025 = 1/362.025 = 2 1/36
![Page 14: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/14.jpg)
Two-Step Inequalities
OBJECTIVE: Solve, graph, and check inequalities that call for two steps to simplify
![Page 15: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/15.jpg)
2x + 20 < 12
x < -4
2x < 12 -202x < -8
Graph the solution.
-1 -2 -3 -4 -5 -6 0
Check. Substitute -4 for x.
2(-4) + 20 < 12-8 + 20 < 12
12 < 12; FalseTherefore, -4 is not a solution.
Solve. Graph and check the solution.
![Page 16: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/16.jpg)
-1 -2 -3 -4 -5 -6 0
Check another value.2(-6) + 20 < 12
-12 + 20 < 128 < 12; True
Therefore, -6 is a solution.
Substitute -6 for x.
Try -10.
2(-10) + 20 < 12-20 + 20 < 12
0 < 12; TrueTherefore, -10 is also a solution.
![Page 17: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/17.jpg)
3a < 16 + 11a
a -2
3a – 11a < 16-8a < 16
Graph the solution.
-1 -2 -3 -4 -5 -6 0
Check. Substitute -2 for a. 3(-2) < 16 + 11(-2)
-6 < 16 -22-6 < -6; False
Solve. Graph and check the solution.
-8 -8>
![Page 18: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/18.jpg)
Graph the solution.
-1 -2 -3 -4 -5 -6 0
Check. Substitute -2 for a. 3(-2) < 16 + 11(-2)
-6 < 16 -22-6 < -6; False
Therefore -2 is not a solution.Substituting 0 for a.
3(0) < 16 + 11(0)
0 < 16 +0 0 < 16 True
Therefore 0 is a solution.
![Page 19: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/19.jpg)
Homework. PB, p119-120Class work. PB, p119
![Page 20: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/20.jpg)
Multistep Inequalities with Grouping symbols
OBJECTIVE: solve, graph, and check the solution of an inequality having a grouping symbols
![Page 21: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/21.jpg)
4(x + 3) -2
Graph the solution.
-6 -7 -8 -9 -10 -11 -5
Solve. Graph and check the solution.
≤ 16 Multiply both sides by -2.
-2 -2
4(x + 3)
- 32≥ Apply the DPMoA.
4x + 12
≥ - 32 Subtract 12 from both sides.- 12 - 12
- 11
4x ≥ Divide both sides by 4 4 4
x ≥
- 44
-4
![Page 22: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/22.jpg)
Graph the solution.
-6 -7 -8 -9 -10 -11 -5 -4
Check the solution. 4(x + 3)
-2≤ 16 Try -11for x.
4(-11 + 3) -2
≤ 16 Combine like terms.
4(-8) -2
≤
16 Multiply.
-32-2
16
≤
Divide
1616 ≤ True, so -11 is a solution.
![Page 23: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/23.jpg)
Graph the solution.
-6 -7 -8 -9 -10 -11 -5 -4
Check the solution. 4(x + 3)
-2≤ 16 Try x = -5.
4(-5 + 3) -2
≤ 16 Combine like terms.
4(-2) -2
≤
16 Multiply.
-8-2
16
≤
Divide
164 ≤ True, so -5 is a solution.
![Page 24: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/24.jpg)
HW: PB, p121-122
Class work PB, p121
![Page 25: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/25.jpg)
Multistep Inequalities :fractions and decimals
solve, graph, and check the solution of an inequality having
fractions and decimals
objective
Pp 114-115, text
![Page 26: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/26.jpg)
(0.12x + 0.36)
-1 -2-3 4 0
Example 1.Solve. Graph and check the solution.
0.6 Multiply both sides by 100.
12
- 36
≥
1
100100
12x + 36 ≥ 60 Subtract 36 from both sides.- 36
12x ≥ 24 Divide both sides by 12.12
x 2≥ Graph.
2 3
0.12x + 0.36 ≥ 0.6 Substitute -2 for x, then evaluate.
![Page 27: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/27.jpg)
0.12x + 0.36 ≥ 0.6 Substitute -2 for x, then evaluate.
0.12(2) + 0.36
≥ 0.6 Multiply.
0.24 + 0.36
≥ 0.6 Add.
0.60
≥ 0.6 True, so 2 is a solution.
0.12x + 0.36
Try 4 for x, then evaluate.
≥ 0.6
0.12(4) + 0.36
≥ 0.6
0.48 + 0.36
≥0.6
Multiply.
Add.
0.84
≥ 0.6 True, so 4 is also a solution.
![Page 28: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/28.jpg)
HW: PB, p125-126
Class work PB, p125
![Page 29: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/29.jpg)
Compound inequalities
OBJECTIVE:
graph and find the solution of compound inequalities
pp 116-117, text
![Page 30: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/30.jpg)
1
2
3
4
5
6 0
Graph: x > 3 and x < 7.
x > 3 Graph on the number line.
8
9
10
7 11
x < 7 Graph on the same number line.
Solution.
The solution set of the compound inequality in shortened form is:
{x | 3 < x < 7}
![Page 31: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/31.jpg)
-2
-1
0
1
2
3 -3
Graph: z ≤ -2 or z ≥ 4.
z ≤ -2 Graph on the number line.
5
6
7
4 8
z ≥ 4 Graph on the same number line.
The solution set of the compound inequality in shortened form is:
{z | z ≤ -2 or z ≥ 4}
![Page 32: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/32.jpg)
Homework. PB, p127-128Class work. PB, p127
![Page 33: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/33.jpg)
Polynomials
OBJECTIVE:
define a polynomial classify a polynomial by the number of its terms simplify polynomials
pp 124-125, text
![Page 34: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/34.jpg)
Do You Remember?
A symbol, usually a letter, used to represent a number
variable
Expressions that contain variables, numbers, and operation symbols
Algebraic Expressions
A term that doesn’t have variables
constant
![Page 35: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/35.jpg)
Do You Remember?
It tells how many times a number or variable called the base is used as a factor.
exponent
A __ of an algebraic expression is a number, a variable, or the product of a number and one or more vaeiables.
term
![Page 36: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/36.jpg)
Remember…
A monomial is an expression that is a number, a variable, or the product of a number and one or more variables with nonnegative exponents. examples:19, m, 7a2, 13xy, 1/4 abc10 Monomials that are real numbers are called constants.
![Page 37: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/37.jpg)
Remember…
A polynomial is a monomial or the sums and/or differences of two or more monomials.
Each monomial in a polynomial is called a termterm..
Polynomials can be classified by their number of termsnumber of terms when they are in simplest formsimplest form.
![Page 38: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/38.jpg)
Remember…
Types ofTypes of PolynomialPolynomial
Name Number of Terms Examples
Monomial
Binomial
Trinomial
1(mono means one)
2(bi means two)
3(tri means three)
2n, 4x3, r, 7, 6x2y5
2x + 8; 3b + p; 2a2 – 8b2
4n + b + c; 2x2 + 8x - 3
![Page 39: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/39.jpg)
Remember…
ClassifyingClassifying Polynomials; Polynomials; before classifying a a polynomial make before classifying a a polynomial make sure it is in its simplest form.sure it is in its simplest form.
Example.Simplify: x2 + 2x + 1 + 3x2 – 4x. Then classify it.
![Page 40: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/40.jpg)
Remember…Example. What kind of a polynomial is
x2 + 2x + 1 + 3x2 – 4x?
x2 + 2x + 1 + 3x2 – 4x
Combine like terms.
4x2 – 2x + 1
Classify.
4x2 – 2x + 1 is a trinomial because it has 3 terms.
![Page 41: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/41.jpg)
Homework. PB, p139-140Class work. text, p125
![Page 42: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/42.jpg)
Modeling Polynomials
OBJECTIVE:
use Algebra tiles to model polynomials
pp 128-129, text
![Page 43: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/43.jpg)
Algebra Tiles
= x2
= -x2
= x
= -x
= 1
= -1
Examples of polynomials and their models.
x2 - 4 -3x2 + 2x +1
![Page 44: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/44.jpg)
Write the polynomials modeled by each set of Algebra tiles.
4x2 + 7x -2x2 – 2x + 9
3x2 + 3x - 5 -3x2 + 2x - 1
![Page 45: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/45.jpg)
If a polynomial is not in simple form, model it with Algebra tiles then combine like tiles.
Example. Simplify 3x2 – 2x – 4 + x2 + 3x.Model the polynomial.
Create zero pairs, (an x tile and a –x tile, and other opposites).
The simple form is 4x2 + x – 4.
Then rearrange the tiles so the like ones are next to each other.
![Page 46: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/46.jpg)
Homework. PB, p143-144Class work. text, p129
![Page 47: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/47.jpg)
Add Polynomials
OBJECTIVES: model the addition of polynomials
add polynomials algebraically
pp 130-131, text
![Page 48: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/48.jpg)
Algebra Tiles
= x2
= -x2
= x
= -x
= 1
= -1
![Page 49: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/49.jpg)
Example. Add 3x2 – 4x + 5 and 2x2 – x – 3.
3x2 - 4x + 5 -2x2 - x - 3
Step 1. Model each polynomial.
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![Page 50: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/50.jpg)
2x2 - x - 3
Step 1. Model each polynomial.
3x2 - 4x + 3
Step 2. Put the same tiles next to each other.
![Page 51: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/51.jpg)
Step 2. Put the same tiles next to each other.
Step 3. Create zero pairs from opposite tiles.
![Page 52: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/52.jpg)
Step 3. Create zero pairs from opposite tiles.
Step 4. Name the remaining tiles for the answer.
x2 - 5x + 2
![Page 53: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/53.jpg)
Example. Add 2x2 + 11x + 9 and 3x2 – 6x
(2x2 + 11x + 9) (3x2 - 6x)
Polynomials can be added algebraically, in either horizontal or vertical form.
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To add polynomials horizontally,use the Commutative and Associative properties to group and combine like terms
Remove parentheses.
2x2 + 11x + 9 + 3x2 - 6x Use the APA and CPA to group and combine like terms 2x2 + 3x2 + 11x – 6x + 9
5x2 + 5x + 9 Answer.
![Page 54: -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =](https://reader035.fdocument.pub/reader035/viewer/2022062802/56649e905503460f94b953ec/html5/thumbnails/54.jpg)
6x2 - 7y2
Example. Add 4x2 + 3xy – 9y2 and 6x2 – 7y2
4x2 + 3xy – 9y2
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To add polynomials vertically, arrange like terms in columns and add the columns separately.
10x2 + - 16y2
Arrange like terms in columns
3xy Answer.