9.1 Adding and Subtracting Polynomials
Presentation
•
Mathematics
•
9th Grade
•
Practice Problem
•
Medium
Standards-aligned
Allison James
Used 36+ times
FREE Resource
12 Slides • 16 Questions
1
Title: 9.1 Adding and Subtracting Polynomials
EQ: How do you know what terms you can add and subtract, and which you can not?
2
What is a polynomial?
The root poly means many
A polynomial is a mathematical expression with many terms
Standard form - written in order from biggest exponent to smallest
once in standard form- the coefficient with the first term is called the Leading Coefficent
This is always a NUMBER not a VARIABLE
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Name by the number of TERMS - how many things are being added or subtracted
Naming Polynomials
Name by the DEGREE- The largest exponent
4
Multiple Choice
Classify by number of terms:
3x3 – 6x
Monomial
Binomial
Trinomial
4-Term Polynomial
5
Multiple Choice
Classify by number of terms:
3x2 – 8x + 1
Monomial
Binomial
Trinomial
4-Term Polynomial
6
Multiple Choice
9x
Monomial
Binomial
Trinomial
4-Term Polynomial
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Like Terms: terms that have the SAME variable(s)
Example: 4x and 17x
Combine Like Terms: take multiple like terms and make them one (By ADDING or SUBTRACTING)
Another word used is SIMPLIFY.
Vocabulary - write this in your notes
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EXAMPLE
Simplify: 10 - 4ab + 2 + 8ab
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Poll
Is this in standard form?
12x+13x3-10
Yes
No
It should be
-10+12x+13x3
No
It should be
13x3+12x-10
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Multiple Choice
What is the leading coefficient?
3x + 5 + 10x4
3
5
10
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Multiple Choice
What is the leading coefficient?
10x - 12x2+15
10
12
-12
15
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Multiple Choice
Combine the like terms in the expression: 5y+2+3y+6
There are no like terms
8y+2+6
53y+12
8y+8
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Adding Polynomials
(Finding the sum)
Method 1
Drop the parentheses.
Combine like terms
*Start with the highest degree*
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EXAMPLE
Simplify by performing the given operation
(3x + 12 - 7y) + (22 - 9x - 13y)
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Multiple Choice
(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
4x3 + 1x2 – 3x + 1
2x3 + 1x2 - 5x + 9
6x3 + 1x - 1x2 - 3
3x5 +1x - 1x5 - 3x
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Multiple Choice
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
11a3 - 4a2 - 14a - 7
5a3 - 4a2 - 14a - 7
5a3 - 4a2 - 20a - 7
5a3 - 9a2 - 20a - 7
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Multiple Choice
9n3 + 4n
7n3 + 6
-3n3 + 2
7n6 + 6
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Multiple Choice
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
2x2 + 3x +1
-2x2 - 11x -4
2x2 + 5x -7
-2x2 + 11x -4
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Subtracting Polynomials
Finding the difference
Method 1
Distribute the negative sign to each term in the 2nd set of parenthesis.
Add/combine like terms like before!
*Start with the highest degree*
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Multiple Choice
-2x3-3x2+7
-2x3+x2+1
2x3-3x3-1
4x3-3x2+7
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Multiple Choice
(x5 + x3) - (6x - x3 + 6x5)
-5x5 + 2x3 - 6x
7x5 - 6x
-5x3 + 2x2 - 6x
-5x5 - 6x
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Multiple Choice
(4x2+ x) - (x2+ 2x)
3x2 - x
4x2 + 2x
3x2 + 3x
3x2 + 2x
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Multiple Choice
9r2+r-5
9r4+r2-4
9r2-r+4
9r2+r-4
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Poll
After today's review, how would you rate your understanding of adding and subtracting polynomials?
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I can explain how to do this. I can teach others. I am an expert.
3
I can do this independently. I have a good understanding.
2
I can do this with help or an example. There are parts I still do not understand
1
I do not understand yet, but am starting to learn. I need help learning this.
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9.1 Homework
Pg.111 #2-26 even
Title: 9.1 Adding and Subtracting Polynomials
EQ: How do you know what terms you can add and subtract, and which you can not?
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