Section 6.3 Special Factoring. Overview In this section we discuss factoring of special polynomials. Special polynomials have a certain number of terms.

Slides:

Advertisements

Similar presentations

Factoring Decision Tree

Advertisements

10.7 Factoring Special Products

Factoring Special Products Goal 1 Recognize Special Products Goal 2 Factor special products using patterns

Factoring GCF’s, differences of squares, perfect squares, and cubes

Special Factoring Formulas

5.4 Special Factoring Techniques

Section 5.4 Factoring FACTORING Greatest Common Factor,

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

Section 5.1 Polynomials Addition And Subtraction.

Factoring Sums & Differences of Cubes

Factoring Special Products Factor perfect square trinomials. 2.Factor a difference of squares. 3.Factor a difference of cubes. 4.Factor a sum of.

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.

(2x) = (2x – 3)((2x)2 + (2x)(3) + (3)2) = (2x – 3)(4x2 + 6x + 9)

Section 6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials.

Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression

6.3 Adding, Subtracting, & Multiplying Polynomials p. 338.

Multiplication: Special Cases Chapter 4.5. Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2.

Factoring Special Products MATH 018 Combined Algebra S. Rook.

factoring special products Formulas to memorize!

Factoring Special Products. Factoring: The reverse of multiplication Use the distributive property to turn the product back into factors. To do this,

2.3 Factor and Solve Polynomial Expressions Pg. 76.

Factoring Special Polynomials(3.8). Perfect Square Trinomials 4x x + 9 4x 2 + 6x + 6x + 9 (4x 2 + 6x) (+6x + 9) (2x + 3) (2x + 3) 2.

Objectives: Students will be able to…  Write a polynomial in factored form  Apply special factoring patterns 5.2: PART 1- FACTORING.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

Do Now 3/12/10 Take out HW from last night. Copy HW in your planner.

Factor the following special cases

Warm-Up #2 Multiply these polynomials. 1) (x-5) 2 2) (8x-1) 2 3. (4x- 3y)(3x +4y) Homework: P5 (1,3,5,11,13,17,27,33,41, 45,49,55,59,63,71,73,77) Answers:

Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 +

Tuesday, July 1 Special Factoring. Difference of Squares Example: m 2 – 64 (m) 2 – (8) 2 (m + 8)(m – 8)

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

Strategies for Factoring

Factoring binomials.

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.

Warm Up:. Factoring Polynomials Number of TermsFactoring TechniqueGeneral Pattern Any number of terms Greatest Common Factora 3 b 2 + 2ab 2 = ab 2 (a.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental.

Section 6.4 Factoring Special Forms. 6.4 Lecture Guide: Factoring Special Forms Objective 1: Factor perfect square trinomials.

Special Cases of Factoring. 1. Check to see if there is a GCF. 2. Write each term as a square. 3. Write those values that are squared as the product of.

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

Difference of Squares Recall that, when multiplying conjugate binomials, the product is a difference of squares. E.g., (x - 7)(x + 7) = x Therefore,

6.3 Adding, Subtracting, & Multiplying Polynomials p. 338 What are the two ways that you can add, subtract or multiply polynomials? Name three special.

5.3 Notes – Add, Subtract, & Multiply Polynomials.

Section 6.4: Factoring Polynomials

Objectives Factor out the greatest common factor of a polynomial.

Copyright © 2013, 2009, 2006 Pearson Education, Inc.

4.5 & 4.6 Factoring Polynomials & Solving by Factoring

Recall (a + b)(a – b) = a2 – b2 Perfect Square Variables x2 = (x)2

Factoring Special Polynomials

Warm - up x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)

What numbers are Perfect Squares?

A Number as a Product of Prime Numbers

Chapter 6 Section 3.

Chapter 4 Review Polynomials.

Factoring Sums & Differences of Cubes

Chapter 6 Section 4.

Polynomials and Polynomial Functions

Factoring Special Products

Special Factoring Formulas & a General Review of Factoring

Polynomials and Polynomial Functions

Keeper 1 Honors Calculus

AA Notes 4.3: Factoring Sums & Differences of Cubes

Unit 5 Factor Special Products

AA-Block Notes 4.4: Factoring Sums & Differences of Cubes

Polynomials and Polynomial Functions

Chapter 6 Section 3.

SECTION 8-4 – MULTIPLYING SPECIAL CASES

Section 9.7 “Factor Special Products”

Chapter 6 Section 3.

Checklist: Factoring Portfolio Page -- Algebra 2

Factoring Polynomials First: Look for a GCF 4 Second: Number of Terms 2 3 Cubes Squares Perfect Square Trinomial Grouping X 2 – 9 X 3 – 27 = (x - 3)

Factoring Polynomials, Special Cases

Presentation transcript:

Section 6.3 Special Factoring

Overview In this section we discuss factoring of special polynomials. Special polynomials have a certain number of terms. The terms have special characteristics. As a result, these special polynomials can be factored by using patterns.

The Difference of Squares a 2 – b 2 = (a + b)(a – b) The first term is a perfect square The last term is a perfect square There is a subtraction sign between the terms 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,… Variables with even exponents The sum of squares, a 2 + b 2, does not factor!

Examples k 2 – 9 36m 2 – 25 32c 2 – 98d 2 (h + k) 2 – 9

The Sum and Difference of Cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) The first term is a perfect cube The last term is a perfect cube 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000,… Variables with exponents that are multiples of 3 The trinomial in the pattern is prime!

Examples y 3 – 64 r g 3 – 27h 3 250x y 3

Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b)(a + b) = (a + b) 2 a 2 – 2ab + b 2 = (a – b)(a – b) = (a – b) 2 The first term is a perfect square The last term is a perfect square The last sign is positive Warning: check it by FOIL! Other trinomial factoring methods will work on these as well.

Examples x x y 2 – 6yz +z 2 (a – b) 2 + 8(a – b) + 16

Don’t Forget!!! Always first look for a GCF!!!!!