# Section 5.1 Polynomials Addition And Subtraction.

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Section 5.1 Polynomials Addition And Subtraction

OBJECTIVES A Classify polynomials.

OBJECTIVES Find the degree of a polynomial and write descending order.

OBJECTIVES C Evaluate a polynomial.

OBJECTIVES D Add or subtract polynomials.

OBJECTIVES E Solve applications involving sums or differences of polynomials.

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

Degree of a Polynomial in Several Variables
DEFINITION Degree of a Polynomial in Several Variables The greatest sum of the exponents of the variables in any one term of the polynomial.

Subtracting Polynomials
RULES Subtracting Polynomials

Chapter 5 Section 5.1A,B Exercise #1

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

Chapter 5 Section 5.1D Exercise #5

METHOD 1

METHOD 2

Chapter 5 Section 5.1D Exercise #6

METHOD 1

METHOD 1

METHOD 1

METHOD 2

Section 5.2 Multiplication of Polynomials

OBJECTIVES A Multiply a monomial by a polynomial.

OBJECTIVES B Multiply two polynomials.

OBJECTIVES C Use the FOIL method to multiply two binomials.

OBJECTIVES D Square a binomial sum or difference.

OBJECTIVES E Find the product of the sum and the difference of two terms.

OBJECTIVES F Use the ideas discussed to solve applications.

Multiplication of Polynomials
RULES Multiplication of Polynomials

USING FOIL To Multiply Two Binomials (x + a)(x + b)

RULE To Square a Binomial Sum

RULE To Square a Binomial Difference

Sum and Difference of Same Two Monomials
PROCEDURE Sum and Difference of Same Two Monomials

Chapter 5 Section 5.2B,C Exercise #8a

METHOD 1

METHOD 2

Chapter 5 Section 5.2D Exercise #9b

Chapter 5 Section 5.2E Exercise #10

Product of Sum and Difference of Same Two Monomials

Section 5.3 The Greatest Common Factor and Factoring by Grouping

OBJECTIVES A Factor out the greatest common factor in a polynomial.

OBJECTIVES B Factor a polynomial with four terms by grouping.

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.

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.

PROCEDURE Factoring by Grouping Group terms with common
factors using the associative property.

PROCEDURE Factoring by Grouping Factor each resulting binomial.

PROCEDURE Factoring by Grouping Factor out the binomial
using the GCF, by the distributive property.

Chapter 5 Section 5.3B Exercise #12

Section 5.4 Factoring Trinomials

OBJECTIVES A Factor a trinomial of the form

OBJECTIVES B Factor a trinomial of the form using trial and error.

OBJECTIVES C Factor a trinomial of the form using the ac test.

PROCEDURE Factoring Trinomials

RULE The ac Test is factorable only if there are two integers
whose product is ac and sum is b.

Chapter 5 Section 5.4A,B,C Exercise #13b

The ac Method Find factors of ac (–20) whose sum is (1) and replace the middle term (xy).

Section 5.5 Special Factoring

OBJECTIVES A Factor a perfect square trinomial.

OBJECTIVES B Factor the difference of two squares.

OBJECTIVES C Factor the sum or difference of two cubes.

Factoring Perfect Square Trinomials
PROCEDURE Factoring Perfect Square Trinomials

Factoring the Difference of
PROCEDURE Factoring the Difference of Two Squares

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

Chapter 5 Section 5.5A Exercise #15a

Chapter 5 Section 5.5 Exercise #16

Difference of Two Squares

Chapter 5 Section 5.5B Exercise #17

Perfect Square Trinomial
Difference of Two Squares

Chapter 5 Section 5.5c Exercise #18a

Sum of Two Cubes

Section 5.6 General Methods of Factoring

OBJECTIVES Factor a polynomial using the procedure given in the text.

PROCEDURE A General Factoring Strategy Factor out the GCF, if
there is one. Look at the number of terms in the given polynomial.

PROCEDURE A General Factoring Strategy
If there are two terms, look for:

PROCEDURE A General Factoring Strategy
If there are two terms, look for:

PROCEDURE A General Factoring Strategy
If there are two terms, look for:

PROCEDURE A General Factoring Strategy
If there are two terms, look for: The sum of two squares, is not factorable.

PROCEDURE A General Factoring Strategy
If there are three terms, look for: Perfect square trinomial

PROCEDURE A General Factoring Strategy
If there are three terms, look for: Trinomials of the form

PROCEDURE A General Factoring Strategy Use the ac method or
trial and error.

PROCEDURE A General Factoring Strategy If there are four terms:
Factor by grouping.

PROCEDURE A General Factoring Strategy Check the result by
multiplying the factors.

Chapter 5 Section 5.6A Exercise #20b

Perfect Square Trinomial

Chapter 5 Section 5.6A Exercise #21

The ac Method Find factors of ac (–12) whose sum is (–11) and replace the middle term (–11xy).

The ac Method Find factors of ac (–12) whose sum is (–11) and replace the middle term (–11xy).

Chapter 5 Section 5.6A Exercise #22

Difference of Two Squares

Section 5.7 Solving Equations by Factoring: Applications

OBJECTIVES A Solve equations by factoring.

OBJECTIVES B Use Pythagorean theorem to find the length of one side of a right triangle when the lengths of the other two sides are given.

OBJECTIVES C Solve applications involving quadratic equations.

PROCEDURE Set equation equal to 0. O Factor Completely. F
Set each linear Factor equal to 0 and solve each. F

DEFINITION Pythagorean Theorem c a b

Chapter 5 Section 5.7A Exercise #23b

O F F or or

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