5.4 Factoring Polynomials Alg 2. The GCF is 5ab. Answer: Distributive Property Factor Factoring with GCF.

Slides:

Advertisements

Similar presentations

Factoring Polynomials.

Advertisements

Factoring Polynomials.

Factoring trinomials ax² + bx +c a = any number besides 1 and 0

Ch. 5 Polynomials, Polynomial Functions, & Factoring

Factoring Polynomials. GCF. Factor by grouping. Factor a trinomial

Factoring Polynomials Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Greatest Common Factor The simplest method.

Factoring Polynomials

Perfect Square Trinomials. Form for Perfect Square Trinomials: a 2 + 2ab + b 2 OR a 2 – 2ab + b 2.

5-4 Factoring Polynomials

Factoring Polynomials

For Common Assessment Chapter 10 Review

EXPONENTS AND POLYNOMIALS College Algebra. Integral Exponents and Scientific Notation Positive and negative exponents Product rule for exponents Zero.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 6 Factoring.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

H.G/1100/061 Factoring a Polynomial and Rational Expressions Lecture #3 Dr.Hayk Melikyan Departmen of Mathematics and CS

UNIT 2 – QUADRATIC, POLYNOMIAL, AND RADICAL EQUATIONS AND INEQUALITIES Chapter 6 – Polynomial Functions 6.6 – Solving Polynomial Equations.

Drill #25 Simplify each expression.. Drill #26 Find the GCF of the following monomials: Factor each polynomial using the GCF:

Factoring a polynomial means expressing it as a product of other polynomials.

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 5.6 Factoring a Polynomial We have looked at factoring out a.

Lesson 9-6 Perfect Squares and Factoring. Determine whether each trinomial is a perfect square trinomial. If so, factor it. Questions to ask. 16x 2 +

Splash Screen. Concept Example 1 Sum and Difference of Cubes A. Factor the polynomial x 3 – 400. If the polynomial cannot be factored, write prime. Answer:The.

Section 4.4 – Factoring Quadratic Expressions Factors of a given number are numbers that have a product equal to the given numbers. Factors of a given.

Copyright © 2011 Pearson Education, Inc. Factoring Polynomials Section P.5 Prerequisites.

Factoring Advanced Algebra Chapter 5. Factoring & Roots  Factors  numbers, variables, monomials, or polynomials multiplied to obtain a product.  Prime.

Factoring Checklist Works every time!. 1. Check to see if there is a GCF. If so, factor it out. 3xy² + 12xy.

Solving Quadratics: Factoring. What is a factor? Numbers you can multiply to get another number 2  3.

Algebra I Review of Factoring Polynomials

2.3 Factor and Solve Polynomial Expressions Pg. 76.

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 4e – Slide #81 A Strategy for Factoring Polynomials A Strategy for Factoring a Polynomial.

Chapter 5 Exponents, Polynomials, and Polynomial Functions.

WARM UP SOLVE USING THE QUADRATIC EQUATION, WHAT IS THE EXACT ANSWER. DON’T ROUND.

Entry Task What is the polynomial function in standard form with the zeros of 0,2,-3 and -1?

FFF FFF i v e o r m s o f a c t o r i n g 1.Greatest Common Factor (GCF) Ex 1 10x 2 y 3 z - 8x 4 y 2 2x 2 y 2 (5yz - 4x 2 ) Ex 2 15a 2 b 5 + 5ab 2 -

Copyright © Cengage Learning. All rights reserved. Factoring Polynomials and Solving Equations by Factoring 5.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

Module 5.4 Factoring. Bell Ringer – End Behavior.

Types of factoring put the title 1-6 on the inside of your foldable and #7 on the back separating them into sum and cubes 1.Greatest Common Factor 2.Difference.

Factoring trinomials ax² + bx +c a = any number besides 1 and 0.

7.6 Polynomials and Factoring Part 2: Factoring. Factoring The process of finding polynomials whose product equals a given polynomial is called factoring.

5-4 Factoring Quadratic Expressions Big Idea: -Factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference.

Adding and Subtracting Polynomials Multiplying Polynomials Factoring Polynomials.

Factoring a polynomial means expressing it as a product of other polynomials.

Try to find the middle through trial and error

Patel – Honors Classes Only Page 243 # Factoring Polynomials 2/6/14 Thursday.

MAIN IDEAS FACTOR POLYNOMIALS. SOLVE POLYNOMIAL EQUATIONS BY FACTORING. 6.6 Solving Polynomial Equations.

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 6.6, Slide 1 Chapter 6 Polynomial Functions.

5-4 Factoring Polynomials

Factor It’s a big deal!.

Module 3.3 Factoring.

Section 6.4: Factoring Polynomials

Factoring Polynomials

Factoring Polynomials

F i v e o r m s o f a c t o r i n g For Forms 1 - 3, do the examples on your paper then use the PowerPoint to check your answers Do not do Form 4.

Factoring Polynomials by Grouping

Factoring Polynomials

Solve a quadratic equation

Factoring Polynomials

Factoring Polynomials

Factoring Trinomials.

4.4 Factoring Polynomials

Answers to Unit 1, Lesson 1 Exercises

Chapter 2: Factoring Chapter 2: Limits Chapter 3: Continuity.

The Greatest Common Factor

4.6 Factoring Polynomials

2.3 Factor and Solve Polynomial Expressions Review (cont.)

Factoring Polynomials.

Unit 12 Rationals (Algebraic)

Checklist: Factoring Portfolio Page -- Algebra 2

Section 9.1 “Properties of Radicals”

Presentation transcript:

5.4 Factoring Polynomials Alg 2

The GCF is 5ab. Answer: Distributive Property Factor Factoring with GCF

Answer: Factor

Group to find the GCF. Factor the GCF of each binomial. Factor Answer: Distributive Property Factoring by Grouping

Answer: Factor

Rewrite problem using –5y and 3y in place of –2y and factor by grouping. To find the coefficient of the y terms, you must find two numbers whose product is 3(–5) or –15 and whose sum is –2. The two coefficients must be 3 and –5 since and Substitute – 5 y + 3 y for – 2 y. Factor Factor out the GCF of each Answer: Distributive Property Associative Property Factoring 2 or 3 terms

Answer: p 2 – 9 is the difference of two squares. Factor out the GCF. Factor Difference of 2 squares

This is the sum of two cubes. Answer: Simplify. Sum of two cubes formula with and Factor Difference of 2 cubes

This polynomial could be considered the difference of two squares or the difference of two cubes. The difference of two squares should always be done before the difference of two cubes. Difference of two squares Answer: Sum and difference of two cubes Factor

Check Use the table feature of your calculator to compare the original expression and the factored form. The table shows that the original function and the factored form have the same function values.

Factor each polynomial. a. b. c. d. Answer:

Summary Techniques for Factoring Polynomials For any number of terms, check for : Greatest Common Factor For two terms, check for: Differences of two squares a 2 - b 2 = (a + b)(a - b) Sum of two cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) Difference of two cubes a 3 - b 3 = (a - b)(a 2 + ab + b 2 ) For three terms, check for: Perfect square trinomials a 2 + 2ab + b 2 = (a + b) 2 a 2 - 2ab + b 2 = (a - b) 2 General Trinomials acx 2 + (ad +bc)x + bd = (ax +b)(cx + d) For four terms, check for: Grouping Ax + bx + ay + by = x(a + b) + y(a + b) = (a + b) (x + y)

Factor the numerator and the denominator. Divide. Assume a  –5, –2. Answer: Therefore, Simplify Quotient of two Trinomials

Simplify Answer: