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 Monomials

A real number, a variable or the product of a real
number and one or more variables with whole
number exponents.
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Algebra 2 CP
 Polynomial

A monomial or a sum of monomials
x
x4

 Degree



3
x5  2 x3  3
A polynomial with the variable x defines the
polynomial function of x.
A polynomial function P(x) in standard form is:
P  x   an x n  an 1 x n 1  ...  a1 x  a0
of a Polynomial (in one variable)
The greatest degree among the monomial terms.

 4y
descending
terms by degree in ___________
numerical order
3x - degree 1
x 2 - degree 2
 Degree
2
 Arranges
(in one variable)
Exponent of the variable


of a Monomial
x2
3x
x  4 - degree 1
x5  2 x3  3
where n is a nonnegative integer and an,…,a0 are
real numbers.
P  x   4 x3  3x 2  5 x  2
- degree 5
Quadratic
Term
Cubic Term
Linear Term
Constant Term
Write each polynomial in standard form. What is the
classification of each by degree? By number of terms?
Degree
Name
Using
Degree
0
Constant
1
Linear
2
3
Quadratic
Cubic
4
Quartic
5
Quintic
3x3  x  5 x 4
3  4 x5  2 x 2  10
Polynomial
Example
Number
of Terms
Name Using
Number of
Terms
5 x 4  3x3  x
Standard Form: __________________
4 x  2 x  13
Standard Form: __________________
5
1
Monomial
Classification
Quartic
(degree): _____________________
Classification
Quintic
(degree): _____________________
x4
2
Binomial
Classification
Trinomial
(terms): _____________________
Classification
Trinomial
(terms): _____________________
Monomial
4 x3  2 x 2  x
1
3
2 x  5x
2
Binomial
4
Polynomial
of 4 Terms
4x
4
2
2
 x5  4 x 2  2 x  1
Trinomial
5
2
3x  4 x3  7 x  3
4x  4x  3
Standard Form: __________________
3
Classification
Cubic
(degree): _____________________
Classification
Trinomial
(terms): _____________________
1
n is even (n≠0)
n is odd (n≠0)
y  4 x3  2 x 2  7
a > 0 Rises to the left, Falls to the left,
a<0
rises to the right rises to the right
Falls to the left, Rises to the left,
Falls to the right falls to the right
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End Behavior:
p  x   4 x 4  4 x 3  24 x 2  x  6
End Behavior:
10
Turning Points:
Rises to the left,
rises to the right
Turning Points:
-10
20
10
Decreasing Interval:
  x  
-20
Decreasing Interval:
-20
The function only decreases.
-40
Increasing Interval:
-10
Increasing Interval:
-30
.02  x  2.14
1.41  x  .02
Rises to the left,
Falls to the right
There are no turning points.
 1.41, 16.1 .02, 6.01
 2.14, 57.08
x  1.41
40
-30
-40
-50
x  2.14
-60
y  x3  1
8
y   x3  2 x 2  x  2
1. Make a table of values.
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1. Make a table of values.
2. Plot points.
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2. Plot points.
x
y
-2
9
-1
2
0
1
1
0
2
7
2
x
y
-2
16
-1
2
0
2
1
2
-2
2
4
-4
4
-2
2
-2
2
-4
-6
-8
-4
-2
2
4
2