Polynomials Add and Subtract - Mrs. Gorman's Math...
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Polynomials Add and Subtract 1 Polynomials Write/Simplify Algebraically and with Algebra Tiles Writing Polynomials A _________ is a number, a variable, or the product of a number and a variable. A ________ is a sum of two monomials. The sum of three monomials is called a _________. monomial binomial trinomial The _________________ is the sum the exponents of all its variables. The __________________ is the greatest degree of any term in the polynomial. degree of a monomial degree of a polynomial
Transcript of Polynomials Add and Subtract - Mrs. Gorman's Math...
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PolynomialsAddandSubtract
1
PolynomialsWrite/SimplifyAlgebraicallyandwithAlgebraTiles
WritingPolynomials
A_________isanumber,avariable,ortheproductofanumberandavariable.A________isasumoftwomonomials.Thesumofthreemonomialsiscalleda_________.
monomial
binomial
trinomial
The_________________isthesumtheexponentsofallitsvariables.The__________________isthegreatestdegreeofanyterminthepolynomial.
degreeofamonomial
degreeofapolynomial
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PolynomialsAddandSubtract
2
Identifyeachasamonomial,binomial,ortrinomial.
x2 12)111
11
x2 13) x x x11
x1)
x x x x
binomialmonomial trinomial
binomialmonomial trinomial
binomialmonomial trinomial
Challenge
Challenge
WritingPolynomials VocabularyMatch
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PolynomialsAddandSubtract
3
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PolynomialsAddandSubtract
4
AddingPolynomials
Drawamodelforeachpolynomial.A)
B)
x2
x2
x
x
11
Whathappenswhenyoucombinethetwoexpressions?
x2 x2 x2 x x 1
x2 x x x x 111
+
+
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PolynomialsAddandSubtract
5
x2x2 xx11
TabTab
Ex.1Ex.1 Ex.3Ex.3 Ex.4Ex.4Ex.2Ex.2
x2x2 xx11x
x
Practice
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Attachments
MultiplyingBinomialsWorksheet.pdf
WritingPolynomialsWorksheet.pdf
AddingPolynomialsWorksheet.pdf
Adding+SubtractingPolynomials.pdf
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Multiplying Binomials Name:
Model each problem using algebra tiles. Write the factors (top and side) equals the sum of tiles.1. 2.
3. 4.
Simplify.5. 2 4 3 5( )( )a b a b 6. 2 4( 12 )(4 )abc a b
7. 43 2
mnm n
8. 2 24
963a bca bc
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Simplify.9. 2 (3 4) 7l l l + 10. 26 (2 3) 5(2 9 3)t t t t +
Solve.11. 3(4 4) 2(5 9)x x+ = + 12. 5(2 1) 3 3(3 2)s s + = +
Simplify using order of operations.13. 30 14 2 14. 5 5 1 3 15. 26 8 3 7+ +
SMART Notebook
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Writing Polynomials using Algebra Tiles Name __________________ Date ________________ Period ___________ Determine a polynomial that represents each model: (note shaded areas are negative) 1. 2. 3. Draw a model for each polygon: 4. 4x 3-
7-
2 +
2x2 + 5. 7x 2x- 2 6. 5x 3x 2+
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Is the polynomial a Monomial, Binomial, or Trinomial? 7. _______________ 8. 6x ________________ 9. 9x __________________ 3 x 8 4x 2+
12x 24 x13x +
2 - 3x7x + 10. 14 __________________ 11. 15x _______________ 12. -x _______________ 2 + Find the degree of each polynomial: 13. degree: _____ 14. 6x degree: _____ 15. 4x9x degree: _____ 3 x2 - 3x7x + 8 2+
24 x13x-x +
16. 14 degree: _____ 17. 15x degree: _____18. degree: _____ 12x2 + Extra Credit: find the degree: 19. degree: _____ 115x 42 +y 2x Arrange each polynomial in descending order: 20. 27 3 - 3x x x+ ________________________ 21. 2 47 2 - 3x x x+ ______________________ 22. _______________________ 23. 26 3 -1x x+ 1 326 5 -8 - 2x x x+ _____________________ 24. 2 34 2 5x x+ + x 11 ______________________ 25. 2 101 2 9 6 3x x x x+ + + __________________
SMART Notebook
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Adding Polynomials Name ________________________
Date ___________________
Period __________________
a) Model each expression, b) Cancel out zero pairs, and c) Write a polynomial in descending order.
1. 2 2(2 5 7) (3 1x x x x + + + + ) = )
2. 2 2(3 4 2) ( 2 1x x x x+ + + =
3. 2 2( 2 5 7) ( 6x x x x + + + 1) = 3 )
4. 2 2( 6 7) (x x x x + =
5. 2 2( 7 10) (6 2x x + + )x = )
6. 2 2(4 2) ( 2 5 3x x x x + + + =
SMART Notebook
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Adding and Subtracting Polynomials
Simplify each expression.
1)
(
5
p
2 3
) +
(
2
p
2 3
p
3
) 2)
(
a
3 2
a
2
)
(
3
a
2 4
a
3
)
3)
(
4
+ 2
n
3
) +
(
5
n
3 + 2
) 4)
(
4
n
3
n
3
)
(
3
n
3 + 4
n
)
5)
(
3
a
2 + 1
)
(
4
+ 2
a
2
) 6)
(
4
r
3 + 3
r
4
)
(
r
4 5
r
3
)
7)
(
5
a
+ 4
)
(
5
a
+ 3
) 8)
(
3
x
4 3
x
)
(
3
x
3
x
4
)
9)
(
4
k
4 + 14
+ 3
k
2
) +
(
3
k
4 14
k
2 8
) 10)
(
3
6
n
5 8
n
4
)
(
6
n
4 3
n
8
n
5
)
11)
(
12
a
5 6
a
10
a
3
)
(
10
a
2
a
5 14
a
4
) 12)
(
8
n
3
n
4 + 10
n
2
)
(
3
n
2 + 11
n
4 7
)
13)
(
x
4 + 13
x
5 + 6
x
3
) +
(
6
x
3 + 5
x
5 + 7
x
4
) 14)
(
9
r
3 + 5
r
2 + 11
r
) +
(
2
r
3 + 9
r
8
r
2
)
15)
(
13
n
2 + 11
n
2
n
4
) +
(
13
n
2 3
n
6
n
4
) 16)
(
7
x
5 + 14
2
x
) +
(
10
x
4 + 7
x
+ 5
x
5
)
17)
(
7
13
x
3 11
x
)
(
2
x
3 + 8
4
x
5
) 18)
(
13
a
2 6
a
5 2
a
)
(
10
a
2 11
a
5 + 9
a
)
-1-
-
19)
(
3
v
5 + 8
v
3 10
v
2
)
(
12
v
5 + 4
v
3 + 14
v
2
) 20)
(
8
b
3 6
+ 3
b
4
)
(
b
4 7
b
3 3
)
21)
(
k
4 3
3
k
3
) +
(
5
k
4 + 6
k
3 8
k
5
) 22)
(
10
k
2 + 7
k
+ 6
k
4
) +
(
14
4
k
4 14
k
)
23)
(
7
n
2 + 8
n
4
)
(
11
n
+ 2
14
n
2
) 24)
(
14
p
4 + 11
p
2 9
p
5
)
(
14
+ 5
p
5 11
p
2
)
25)
(
8
k
+
k
2 6
)
(
10
k
+ 7
2
k
2
)
26)
(
9
v
2 8
u
) +
(
2
uv
2
u
2 +
v
2
) +
(
v
2 + 4
uv
)
27)
(
4
x
2 + 7
x
3y
2
)
(
6
x
2 7
x
3y
2 4
x
)
(
10
x
+ 9
x
2
)
28)
(
5
u
3v
4 + 9
u
) +
(
5
u
3v
4 8
u
+ 8
u
2v
2
) +
(
8
u
4v
2 + 8
u
3v
4
)
29)
(
9
xy
3 9
x
4y
3
) +
(
3
xy
3 + 7
y
4 8
x
4y
4
) +
(
3
x
4y
3 + 2
xy
3
)
30)
(
y
3 7
x
4y
4
) +
(
10
x
4y
3 + 6
y
3 + 4
x
4y
4
)
(
x
4y
3 + 6
x
4y
4
)
-2-
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Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Adding and Subtracting Polynomials
Simplify each expression.
1)
(
5
p
2 3
) +
(
2
p
2 3
p
3
)
3
p
3 + 7
p
2 3
2)
(
a
3 2
a
2
)
(
3
a
2 4
a
3
)
5
a
3 5
a
2
3)
(
4
+ 2
n
3
) +
(
5
n
3 + 2
)
7
n
3 + 6
4)
(
4
n
3
n
3
)
(
3
n
3 + 4
n
)
6
n
3
5)
(
3
a
2 + 1
)
(
4
+ 2
a
2
)
a
2 3
6)
(
4
r
3 + 3
r
4
)
(
r
4 5
r
3
)
2
r
4 + 9
r
3
7)
(
5
a
+ 4
)
(
5
a
+ 3
)
1
8)
(
3
x
4 3
x
)
(
3
x
3
x
4
)
6
x
4 6
x
9)
(
4
k
4 + 14
+ 3
k
2
) +
(
3
k
4 14
k
2 8
)
7
k
4 11
k
2 + 6
10)
(
3
6
n
5 8
n
4
)
(
6
n
4 3
n
8
n
5
)
2
n
5 2
n
4 + 3
n
+ 3
11)
(
12
a
5 6
a
10
a
3
)
(
10
a
2
a
5 14
a
4
)
14
a
5 + 14
a
4 10
a
3 16
a
12)
(
8
n
3
n
4 + 10
n
2
)
(
3
n
2 + 11
n
4 7
)
14
n
4 + 7
n
2 + 8
n
+ 7
13)
(
x
4 + 13
x
5 + 6
x
3
) +
(
6
x
3 + 5
x
5 + 7
x
4
)
18
x
5 + 6
x
4 + 12
x
3
14)
(
9
r
3 + 5
r
2 + 11
r
) +
(
2
r
3 + 9
r
8
r
2
)
7
r
3 3
r
2 + 20
r
15)
(
13
n
2 + 11
n
2
n
4
) +
(
13
n
2 3
n
6
n
4
)
8
n
4 + 8
n
16)
(
7
x
5 + 14
2
x
) +
(
10
x
4 + 7
x
+ 5
x
5
)
2
x
5 + 10
x
4 + 5
x
+ 14
17)
(
7
13
x
3 11
x
)
(
2
x
3 + 8
4
x
5
)
4
x
5 15
x
3 11
x
1
18)
(
13
a
2 6
a
5 2
a
)
(
10
a
2 11
a
5 + 9
a
)
5
a
5 + 23
a
2 11
a
-1-
-
19)
(
3
v
5 + 8
v
3 10
v
2
)
(
12
v
5 + 4
v
3 + 14
v
2
)
15
v
5 + 4
v
3 24
v
2
20)
(
8
b
3 6
+ 3
b
4
)
(
b
4 7
b
3 3
)
2
b
4 + 15
b
3 3
21)
(
k
4 3
3
k
3
) +
(
5
k
4 + 6
k
3 8
k
5
)
8
k
5 4
k
4 + 3
k
3 3
22)
(
10
k
2 + 7
k
+ 6
k
4
) +
(
14
4
k
4 14
k
)
2
k
4 10
k
2 7
k
14
23)
(
7
n
2 + 8
n
4
)
(
11
n
+ 2
14
n
2
)
7
n
2 + 19
n
6
24)
(
14
p
4 + 11
p
2 9
p
5
)
(
14
+ 5
p
5 11
p
2
)
14
p
5 + 14
p
4 + 22
p
2 + 14
25)
(
8
k
+
k
2 6
)
(
10
k
+ 7
2
k
2
)
3
k
2 + 18
k
13
26)
(
9
v
2 8
u
) +
(
2
uv
2
u
2 +
v
2
) +
(
v
2 + 4
uv
)
9
v
2 + 2
uv
2
u
2 8
u
27)
(
4
x
2 + 7
x
3y
2
)
(
6
x
2 7
x
3y
2 4
x
)
(
10
x
+ 9
x
2
)
14
x
3y
2 +
x
2 6
x
28)
(
5
u
3v
4 + 9
u
) +
(
5
u
3v
4 8
u
+ 8
u
2v
2
) +
(
8
u
4v
2 + 8
u
3v
4
)
2
u
3v
4 8
u
4v
2 + 8
u
2v
2 +
u
29)
(
9
xy
3 9
x
4y
3
) +
(
3
xy
3 + 7
y
4 8
x
4y
4
) +
(
3
x
4y
3 + 2
xy
3
)
8
x
4y
4 6
x
4y
3 + 7
y
4 4
xy
3
30)
(
y
3 7
x
4y
4
) +
(
10
x
4y
3 + 6
y
3 + 4
x
4y
4
)
(
x
4y
3 + 6
x
4y
4
)
9
x
4y
4 11
x
4y
3 + 7
y
3
-2-
SMART Notebook
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