WarmUp

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Warm-Up
Evaluate each expression for x -2.
1) -x 1
2) x2 - 5
3) -(x 6)
Simplify each expression.
4) (x 5) (2x 3)
5) (x 9) (4x 6)
6) (-x2 2) (x2 2)
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7.1 An Intro to Polynomials

• Objectives
• Identify, evaluate, add, and subtract polynomials
• Classify polynomials, and describe the shapes of
  their graphs

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Definitions for Polynomials

• Monomial a numeral, variable, or the product of
  a numeral and one or more variables
• Ex
• Constant a monomial w/ no variables
• Ex
• Coefficient numerical factor in a monomial
• Ex
• Degree of a Monomial sum of exponents of its
  variables
• Ex See Below

NOT QUOTIENT! i.e. x cant be on bottom!!!!
Give the degree for the following
monomial. 4x2y3z _________ ab4c2 ________
8 ________
7
6
0
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Definitions for Polynomials

• Polynomial is many (more than 1) monomials
  connected by addition or subtraction.

(5x 4)
(2x2 3x 2)
Binomial - ___________ Trinomial - ______________

• Degree of the Polynomial is the degree of
  its highest monomial term

Example Give the degree of the
polynomial. 4x3 6x2 -8x5 6 ________
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Classification of a Polynomial
n 0
constant
3
linear
n 1
5x 4
quadratic
n 2
2x2 3x - 2
cubic
n 3
5x3 3x2 x 9
quartic
3x4 2x3 8x2 6x 5
n 4
-2x5 3x4 x3 3x2 2x 6
n 5
quintic
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Example 1
Classify each polynomial by degree and by number
of terms.
a) 5x 2x3 2x2
cubic trinomial
b) x5 4x3 x5 3x2 4x3
quadratic monomial
c) x2 4 8x 2x3
cubic polynomial
quintic trinomial
d) 3x3 2x x3 6x5
7th degree binomial
e) 2x 5x7
Not a polynomial
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Example 2
Add - Write your answer in standard form. 1.
(5x2 3x 4) (3x2 5)
2. (6x3 3x2 4) (10 3x 5x2 2x3)
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Example 3
Subtract Write your answer in standard
form. (5x2 6x 11) (-8x3 x2 2)
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Example 4
Subtract. (2x2y2 3xy3 4y4) - (x2y2 5xy3
3y 2y4)
2x2y2 3xy3 4y4
- x2y2 5xy3 3y 2y4
x2y2
8xy3
2y4
3y
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Example 5

• Evaluate
• x2 4x3 3 for x 2
• 3x3 - 2x2 x 4 for x -1

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Example 6
If the cubic function C(x) 3x3 15x 15 gives
the cost of manufacturing x units (in thousands)
of a product, what is the cost to manufacture
10,000 units of the product?
C(x) 3x3 15x 15
C(10) 3(10)3 15(10) 15
C(10) 3000 150 15
C(10) 2865
2865
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Graphs of Polynomial Functions
A polynomial function is a function that is
defined by a polynomial function
Graph each function below. (in your calc.)
n2 u shaped, ends up n3 s shaped, Lt
down, Rt up n3 s shaped, Lt up, Rt
down n4 w shaped, Lt up, Rt up n4 m
shaped, Lt down, Rt down
y x2 x - 2
y 3x3 12x 4
y -2x3 4x2 x - 2
y x4 5x3 5x2 x - 6
y -x4 6x3 5x2 6x
Make a conjecture about the degree of a function
and the end behavior of the graph.
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Example 7
Graph each function. Describe its general shape.
a) P(x) 2x3 - 1
b) Q(x) -3x4 2
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Homework

• Pg 429 4 - 10, 11 57 odd
• Pg 956 9 16 all