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Vocab
The Polynomials correctly
identified!!
Monomial Binomial Trinomial ­8
3x3 ­ 7
4abc ­ 3 ­ y
­5x2
5x2 + x
x + y ­ 7
4abc
4abc ­ x
5x2 + x + 7
Which of the above are polynomials?
All are polynomials!
ID Poly Answers
1
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Degree of a Polynomial
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The nomial by d mo
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Steps for finding the degree
of any Polynomial
1. Find the degree of each
term (monomial)
2. Degree = biggest # of
exponents
Example: 5x2
Degree:
Type: Monomial
2 b/c x2 means
there are "2" x's
Degree of a Polynomial
Determine the type of Polynomial,
then find it's degree
Type
Degree
4ab3c2
­9
8x3 + xy
Monomial
Monomial
Binomial
6
b/c there is
1 "a", 3 "b"s and 2 "c"s
(1+3+2=6)
0
b/c there are
NO variables
3
b/c there are 3 "x"s
in the first term and
1 "x" + 1 "y" in the
2nd. Biggest # wins!
Degree Answers
2
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Determine the type of Polynomial,
then find it's degree
8x3 +4x2y ­ xy
Type
Degree
6x2 y+5x3 y2 z+x2 y2 ­x5
Polynomial
Trinomial
3
6
All 3 terms have
a degree of 3
1 term degree = 3
2nd term degree = 6
st
3rd term degree = 4
4th term degree = 5
BIGGEST # WINS!
So... Degree = 6
More Answers
Order of a Polynomial
Ascending Order
Terms are arranged so that the degree
is in order from low to high
Descending Order
Terms are arranged so that the degree
is in order from high to low
Order
3
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3 + 5a ­ 8a2 + a3
Type:
Polynomial
(b/c more than 3 terms)
Degree:
3
(b/c last term has 3 a's)
Order:
Ascending
(b/c a's go from low to high)
Write in Opposite Order:
a3 - 8a2 + 5a + 3
(Descending = high to low)
Order Example #1
y3 ­ 3xy2 + 3x2y ­ x3
Type:
Degree:
Polynomial
3 (all terms have a degree = 3)
Order for "x":
Ascending
Order for "y":
Descending
Descending order for "x":
-x3 + 3x2y - 3xy2 + y3
Descending order for "y":
y3 - 3xy2 + 3x2y - x3
Order Example #2
4
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Middle School Math Review:
3
+ 2
5
3x
+ 2x
5x
3x
2x
+ 3
5x + 3
Middle School Math
Middle School Math Review:
How do you solve:
(2x + 8) + (x - 3)
Middle School Math
5
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Steps for Adding Polynomials
1. Identify like terms
2. Combine coefficients of like terms
a. If signs are the same ADD and take sign of larger
b. If signs are different subtract and take sign of larger
Steps for Adding Examples:
1. (9y ­ 7x + 15z) + (8x ­ 8z ­ 3y)
2. (2x 2 ­ 5x) + (3x 2 + x)
6y + x + 7z
5x2 - 4x
Adding Examples
6
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Additive Inverse:
"-a" is the additive inverse of "a" if
a + (-a) = 0
In other words:
a and -a cancel each other out!
Additive Inverse
State the Additive Inverse of each Polynomial
1. x + 2y
2. 2x2 ­ 3x + 5
-x - 2y
-2x2 + 3x - 5
3. ­8x + 5y ­ 7z
4. 3x3 ­ 2x2 ­ 5x
8x - 5y + 7z
-3x3 + 2x2 + 5x
Additive Inverse Examples
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Steps for Subtracting Polynomials
1. Distribute the negative
(change 2nd parenthesis to the additive inverse)
2. Identify like terms
3. Combine coefficients of like terms
a. If signs are the same - ADD and take sign of larger
b. If signs are different -SUBT. and take sign of larger
Steps for Subtracting Examples:
1. (4y2 ­ 3y) ­ (6y2 + 5y + 7)
-2y2 - 8y - 7
2. (5x2­4x+7) ­ (2x2­3x+3)
3x2 - x + 4
3. 5x2 ­ 4x + 7 ­ 2x2 ­ 3x + 3
3x2 - 7x + 10
Subtracting Examples
8
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Homework:
Worksheet 8-1
Homework
9