Polynomials Addition And Subtraction

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Section 5.1
Polynomials Addition And Subtraction
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITION
Degree of a Polynomial in One Variable

The degree of a polynomial in one variable is the
greatest exponent of that variable.
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DEFINITION
Degree of a Polynomial in Several Variables

The greatest sum of the exponents of the
variables in any one term of the polynomial.
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RULES
Properties for Adding Polynomials

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RULES
Properties for Adding Polynomials

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RULES
Properties for Adding Polynomials

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RULES

Subtracting Polynomials
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Section 5.1A,B
Chapter 5

• Exercise 1

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Classify as a monomial, binomial, or trinomial
and give the degree.
Binomial.
Degree is determined by comparing
Degree 8
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Section 5.1D
Chapter 5

• Exercise 5

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METHOD 1
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METHOD 2
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Section 5.1D
Chapter 5

• Exercise 6

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METHOD 1
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METHOD 1
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METHOD 1
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METHOD 2
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Section 5.2
Multiplication of Polynomials
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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RULES
Multiplication of Polynomials

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USING FOIL
To Multiply Two Binomials
(x a)(x b)
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RULE
To Square a Binomial Sum
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RULE
To Square a Binomial Difference
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PROCEDURE
Sum and Difference of Same Two Monomials

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Section 5.2B,C
Chapter 5

• Exercise 8a

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METHOD 1
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METHOD 2
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Section 5.2D
Chapter 5

• Exercise 9b

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(No Transcript)
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Section 5.2E
Chapter 5

• Exercise 10

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Product of Sum and Difference ofSame Two
Monomials
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Section 5.3
The Greatest Common Factor and Factoring by
Grouping
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OBJECTIVES
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OBJECTIVES
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GREATEST COMMON FACTOR
is the Greatest Common monomial Factor
(GCF) of a polynomial in x if
1. a is the greatest integer that divides each
coefficient.
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GREATEST COMMON FACTOR
is the Greatest Common monomial Factor
(GCF) of a polynomial in x if
2. n is the smallest exponent of x in all the
terms.
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PROCEDURE

Factoring by Grouping

• Group terms with common
• factors using the
• associative property.

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PROCEDURE

Factoring by Grouping

• Factor each resulting
• binomial.

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PROCEDURE

Factoring by Grouping

• Factor out the binomial
• using the GCF, by the
• distributive property.

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Section 5.3B
Chapter 5

• Exercise 12

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(No Transcript)
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Section 5.4
Factoring Trinomials
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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PROCEDURE
Factoring Trinomials

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RULE

The ac Test
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Section 5.4A,B,C
Chapter 5

• Exercise 13b

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The ac Method Find
factors of ac (20) whose sum is (1) and replace
the middle term (xy).
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Section 5.5
Special Factoring
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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PROCEDURE
Factoring Perfect Square Trinomials

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PROCEDURE

Factoring the Difference of Two Squares
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PROCEDURE
Factoring the Sum and Difference of Two Cubes

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Section 5.5A
Chapter 5

• Exercise 15a

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(No Transcript)
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Section 5.5
Chapter 5

• Exercise 16

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Difference of Two Squares
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Section 5.5B
Chapter 5

• Exercise 17

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Perfect Square Trinomial
Difference of Two Squares
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Section 5.5c
Chapter 5

• Exercise 18a

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Sum of Two Cubes
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Section 5.6
General Methods of Factoring
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OBJECTIVES
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PROCEDURE
A General Factoring Strategy

• Factor out the GCF, if
• there is one.

• Look at the number of terms
• in the given polynomial.

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PROCEDURE
A General Factoring Strategy
If there are two terms, look for
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PROCEDURE
A General Factoring Strategy
If there are two terms, look for
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PROCEDURE
A General Factoring Strategy
If there are two terms, look for
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PROCEDURE
A General Factoring Strategy
If there are two terms, look for
The sum of two squares, is
not factorable.
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PROCEDURE
A General Factoring Strategy
If there are three terms, look for
Perfect square trinomial
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PROCEDURE
A General Factoring Strategy
If there are three terms, look for
Trinomials of the form
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PROCEDURE
A General Factoring Strategy
Use the ac method or trial and error.
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PROCEDURE
A General Factoring Strategy
If there are four terms
Factor by grouping.
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PROCEDURE
A General Factoring Strategy

• Check the result by
• multiplying the factors.

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Section 5.6A
Chapter 5

• Exercise 20b

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Perfect Square Trinomial
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Section 5.6A
Chapter 5

• Exercise 21

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The ac Method
Find
factors of ac (12) whose sum is (11) and
replace the middle term (11xy).
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The ac Method
Find
factors of ac (12) whose sum is (11) and
replace the middle term (11xy).
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Section 5.6A
Chapter 5

• Exercise 22

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Difference of Two Squares
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Section 5.7
Solving Equations by Factoring Applications
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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PROCEDURE
O

1. Set equation equal to 0.

1. Factor Completely.

F

• Set each linear Factor
• equal to 0 and solve each.

F
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DEFINITION
Pythagorean Theorem

c
a
b
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Section 5.7A
Chapter 5

• Exercise 23b

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O
F
F