Factoring Difference of Two Squares

Slides:

Advertisements

Similar presentations

Factoring Trinomials of the form x 2 + bx + c Chapter 5.3.

Advertisements

Factoring Decision Tree

© 2007 by S - Squared, Inc. All Rights Reserved.

MTH Algebra Special Factoring Formulas and a General Review of Factoring Chapter 5 Section 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.

Warm Up Factor each expression. 1. 3x – 6y 3(x – 2y) 2. a2 – b2

§ 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.

Factoring and Solving Polynomial Equations (Day 1)

Factoring a Binomial There are two possibilities when you are given a binomial. It is a difference of squares There is a monomial to factor out.

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.

Multiplying Polynomials *You must know how to multiply before you can factor!”

Factoring - Difference of Squares What is a Perfect Square.

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

Aim: How do we factor polynomials completely? Do Now: Factor the following 1. 2x 3 y 2 – 4x 2 y 3 2. x 2 – 5x – 6 3. x 3 – 5x 2 – 6x.

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

Strategies for Factoring

Bellwork: Factor Each. 5x2 + 22x + 8 4x2 – 25 81x2 – 36 20x2 – 7x – 6

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 Day 2 Unit 3A. Use FOIL to Simplify: 1. (x-2)(x+2) 2. (5x + 6)(5x – 6) 3. (x -3)(x+3) 4. (x-1)(x+1)

Objectives Factor the sum and difference of two cubes.

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

Multiplying Conjugates The following pairs of binomials are called conjugates. Notice that they all have the same terms, only the sign between them is.

ALGEBRA 1 Lesson 8-7 Warm-Up ALGEBRA 1 “Factoring Special Cases” (8-7) What is a “perfect square trinomial”? How do you factor a “perfect square trinomial”?

4-3 Equivalent Expressions Learn factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 x - 4 x2x2.

5.3 Notes – Add, Subtract, & Multiply Polynomials.

Notes Over 10.8 Methods of Factoring Binomial Trinomial

Multiply (x+3)(2x-7) Factor 3. 42x – 7

Objectives Factor out the greatest common factor of a polynomial.

using the Diamond or "ac" method

Chapter 6 Section 4.

4.5 & 4.6 Factoring Polynomials & Solving by Factoring

Factoring By Grouping and Cubes.

Algebra II with Trigonometry Mrs. Stacey

Warm Up Factor each expression. 1. 3x – 6y 3(x – 2y) 2. a2 – b2

8-4 Special Products of Polynomials

Lesson 9.3 Find Special Products of Polynomials

What numbers are Perfect Squares?

Factoring Polynomials

8.6 Choosing a Factoring Method

FACTORING BINOMIALS Section 4.3

Chapter 6 Section 4.

Multiply (x + 3) (x + 6) (x + 2) (x + 9) (x + 1) (x + 18)

Factoring Polynomials.

Warm-up Factor:.

Factoring Special Cases

Warm – Up #1 What do you find in common with the following algebraic expression? 2

Example 2A: Factoring by GCF and Recognizing Patterns

Example 1A: Factoring Trinomials by Guess and Check

Algebra 1 Section 10.3.

Factoring Special Cases

Factoring Special Cases

Factoring Special Cases

Section 5.5 Factoring Polynomials

Warm Up: Solve the Equation 4x2 + 8x – 32 = 0.

Factoring by GCF CA 11.0.

Factoring by GCF CA 11.0.

Factoring the Difference of

Sign Rule: When the last term is NEGATIVE…

Sign Rule: When the last term is POSITIVE…

Chapter 6 Section 4.

Factoring Trinomials.

Factoring Trinomials and Difference of Two Perfect Squares

Factoring Polynomials.

Factoring Polynomials.

2.3 Factor and Solve Polynomial Expressions

Algebra II with Trigonometry Mr. Agnew

Exponent Rules, Multiplying Polynomials, and GCF Factoring

Factoring by Grouping Objective: After completing this section, students should be able to factor polynomials by grouping. After working through this.

Presentation transcript:

Factoring Difference of Two Squares

What Numbers are Perfect Squares? List the first 20 Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400

Factoring: Difference of Two Squares Count the number of terms. Is it a binomial? Is the first term a perfect square? Is the last term a perfect square? Is it, or could it be, a subtraction of two perfect squares? x2 – 9 = (x + 3)(x – 3) The sum of squares will not factor a2 + b2

Using FOIL we find the product of two binomials.

Rewrite the polynomial as the product of a sum and a difference.

Conditions for Difference of Squares Must be a binomial with subtraction. First term must be a perfect square. (x)(x) = x2 Second term must be a perfect square (6)(6) = 36

Check for GCF. Sometimes it is necessary to remove the GCF before it can be factored more completely.

Removing a GCF of -1. In some cases removing a GCF of negative one will result in the difference of squares. Alternate Method Now you can use algebra to show that they are equivalent

Difference of Two Squares You Try

Factoring - Difference of Squares