Transcript 3.2 Adding and Subtracting Polynomials

Bell Ringer

Write an English sentence for the
mathematical expression

Write an algebraic expression for the
statement

1
Ten monkeys plus seventeen
bananas
Bell Ringer!

2
Pull out notes, write down as many
English words as you can for each
sign:
3
4
Homework

5 minutes to complete

Correct. Out of 32!
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Add and Subtract Polynomials
Review
x+x
2x
x·x
2
x
2x + 3x
2x·3x
5x
2
6x
2
4x
+ 4x
NOT
LIKE
TERMS!
2
4x ·4x
3
16x
2
5x
+
2
6x
2
x
2
2
5x ·x
4
5x
Adding/Subtracting Polynomials
• We will discuss three methods
– Algebra Tiles
– Vertical Method
– Horizontal Method
Algebra Tiles
Algebra tiles can be used to model
operations involving integers.
 Let the small green square represent
+1 and the small pink square
represent -1.

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The green and pink squares are
additive inverses of each other.
Algebra Tiles
Algebra tiles can be used to model
operations involving variables.
 Let the green rectangle represent +1x
or x and the pink rectangle represent 1 x or -x .

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The green and red rods are additive
inverses of each other.
Algebra Tiles
Let the green square represent x2. The pink
square represents -x2.
 As with integers, the green squares and the
pink squares form a zero pair.
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Modeling with Algebra Tiles
2x + 3
4x – 2
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Zero Pairs
Called zero pairs because they are
additive inverses of each other.
 When put together, they model zero.

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Practice with Integers
Algebra tiles can be use to model
adding, subtracting, multiplying, and
dividing real numbers.
 Remember, if you don’t have enough
of something, you can add “zero
pairs”
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Modeling Addition/Subtraction
-2 – 3
 Start with -2

Take away positive 3. But wait, I don’t
have 3 so I must add zero pairs!
 Now remove positive 3
 You are left with -5
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Adding Polynomials
(2x + 4) + (x + 1) = 3x + 5
Combine like terms to get three
x’s and five positive ones
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Activity Sheet
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Find question 4
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Work through the worksheet
as partners
We will discuss two other ways to
think about adding/subtracting next.
 Every group needs to answer
questions 1-6 completely.
 Attempt Question 7.
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Adding and Subtracting
Polynomials
(3x4 – 5x2 + 1) + (6x4 + 2x2 – 7)
4
9x
–
2
3x
–6
(r2 + 2r – 3) + (3r2 – r – 1)
2
4r
+r –4
(-2a5 – 2a4 + 7a) + (6a4 + 2a2 – 2a)
5
-2a +
4
4a
+
2
2a
+ 5a
(-c5 + 8c + 2) – (-2c5 + 6c – 1)
–
5
(-c
+ 8c + 2) +
5
c
5
(2c
– 6c + 1)
+ 2c + 3
If you haven’t already finished question
7, finish it then turn it in.
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Bulls Eye
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Homework: Worksheet
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