Section 5 1 Polynomials Addition And Subtraction OBJECTIV
Section 5. 1 Polynomials Addition And Subtraction
OBJECTIV ES A Classify polynomials.
OBJECTIV ES B Find the degree of a polynomial and write descending order.
OBJECTIV ES C Evaluate a polynomial.
OBJECTIV ES D Add or subtract polynomials.
OBJECTIV ES E Solve applications involving sums or differences of polynomials.
DEFINITION Degree of a Polynomial in One Variable The degree of a polynomial in one variable is the greatest exponent of that
DEFINITION Degree of a Polynomial in Several Variables The greatest sum of the exponents of the variables in any one term of the polynomial.
RULES Properties for Adding Polynomials
RULES Properties for Adding Polynomials
RULES Properties for Adding Polynomials
RULES Subtracting Polynomials
Chapter 5 Section 5. 1 A, 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. 1 D Exercise #5
METHOD 1
METHOD 2
Chapter 5 Section 5. 1 D Exercise #6
METHOD 1
METHOD 1
METHOD 1
METHOD 2
Section 5. 2 Multiplication of Polynomials
OBJECTIV ES A Multiply a monomial by a polynomial.
OBJECTIV ES B Multiply two polynomials.
OBJECTIV ES C Use the FOIL method to multiply two binomials.
OBJECTIV ES D Square a binomial sum or difference.
OBJECTIV ES E Find the product of the sum and the difference of two terms.
OBJECTIV ES F Use the ideas discussed to solve applications.
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
PROCEDURE Sum and Difference of Same Two Monomials
Chapter 5 Section 5. 2 B, C Exercise #8 a
METHOD 1
METHOD 2
Chapter 5 Section 5. 2 D Exercise #9 b
Chapter 5 Section 5. 2 E Exercise #10
Product of Sum and Difference of Same Two Monomials
Section 5. 3 The Greatest Common Factor and Factoring by Grouping
OBJECTIV ES A Factor out the greatest common factor in a polynomial.
OBJECTIV ES 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 is the. FACTOR 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 1. Group terms with commo 2. factors using the 3. associative property.
PROCEDURE Factoring by Grouping 2. Factor each resulting 3. binomial.
PROCEDURE Factoring by Grouping 3. Factor out the binomial 4. using the GCF, by the 5. distributive property.
Chapter 5 Section 5. 3 B Exercise #12
Section 5. 4 Factoring Trinomials
OBJECTIV ES A Factor a trinomial of the form.
OBJECTIV ES B Factor a trinomial of the form using trial and error.
OBJECTIV ES C Factor a trinomial of the form using the ac test.
PROCEDURE Factoring Trinomials
RULE The ac Test is factorable on if there are two integers whose product is ac and sum is b.
Chapter 5 Section 5. 4 A, B, C Exercise #13 b
The ac Method Find factors of ac (– 20) whose sum is (1) and replace the middle term (xy).
Section 5. 5 Special Factoring
OBJECTIV ES A Factor a perfect square trinomial.
OBJECTIV ES B Factor the difference of two squares.
OBJECTIV ES C Factor the sum or difference of two cubes.
PROCEDURE Factoring Perfect Square Trinomials
PROCEDURE Factoring the Difference of Two Squares
PROCEDURE Factoring the Sum and Difference of Two Cubes
Chapter 5 Section 5. 5 A Exercise #15 a
Chapter 5 Section 5. 5 Exercise #16
Difference of Two Squares
Chapter 5 Section 5. 5 B Exercise #17
Perfect Square Trinomial Difference of Two Squares
Chapter 5 Section 5. 5 c Exercise #18 a
Sum of Two Cubes
Section 5. 6 General Methods of Factoring
OBJECTIV ES A Factor a polynomial using the procedure given in the text.
PROCEDURE A General Factoring Strategy 1. Factor out the GCF, if 2. there is one. 2. Look at the number of terms 3. in the given
PROCEDURE A General Factoring Strategy If there are two terms, look f
PROCEDURE A General Factoring Strategy If there are two terms, look f
PROCEDURE A General Factoring Strategy If there are two terms, look f
PROCEDURE A General Factoring Strategy If there are two terms, look f The sum of two squares, is not factorable.
PROCEDURE A General Factoring Strategy If there are three terms, look Perfect square trinomial
PROCEDURE A General Factoring Strategy If there are three terms, look 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 3. Check the result by 4. multiplying the factors.
Chapter 5 Section 5. 6 A Exercise #20 b
Perfect Square Trinomial
Chapter 5 Section 5. 6 A Exercise #21
The ac Method Find factors of ac (– 12) whose sum is (– 11) and replace the middle term (– 11 xy).
The ac Method Find factors of ac (– 12) whose sum is (– 11) and replace the middle term (– 11 xy).
Chapter 5 Section 5. 6 A Exercise #22
Difference of Two Squares
Section 5. 7 Solving Equations by Factoring: Applications
OBJECTIV ES A Solve equations by factoring.
OBJECTIV ES B Use Pythagorean theorem to find the length of one side of a right triangle when the lengths of the other two sides are
OBJECTIV ES C Solve applications involving quadratic equations.
PROCEDURE 1. Set equation equal to. O 0. 2. Factor Completely. F 3. Set each linear Factor. F equal to 0 and solve each.
DEFINITION Pythagorean Theorem a c b
Chapter 5 Section 5. 7 A Exercise #23 b
O F F or or
- Slides: 101
