factoring special products Formulas to memorize!

Slides:

Advertisements

Similar presentations

10.7 Factoring Special Products

Advertisements

Bellwork Keep it :) Factor by grouping 1. 2xy - x 2 y x 2. 3m 2 + 9m + km + 3k.

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

Special Factoring Formulas

5.4 Special Factoring Techniques

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

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

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.

Chapter 8: Factoring.

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

Sullivan Algebra and Trigonometry: Section R.5 Factoring Objectives of this Section Factor the Difference of Two Squares Factor the Sum and Difference.

Factoring Review Review Tying it All Together Shortcut for the Shortcuts.

Algebra II Factoring Strategy 1 Learning these guidelines has been directly linked to greater Algebra success!! Part1Part 2Part 3Part 4 I.Always look.

Special Cases of Factoring Chapter 5.5 Perfect Square Trinomials a 2 + 2ab + b 2 (a + b) 2 = a 2 – 2ab + b 2 (a – b) 2 =

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.

Algebra II Factoring Strategy 1 Learning these guidelines has been directly linked to greater Algebra success!! Part1Part 2Part 3Part 4 I.Always look.

Factoring Special Products MATH 018 Combined Algebra S. Rook.

Special Products Difference of Two Squares Perfect Square Trinomials

2.3 Factor and Solve Polynomial Expressions Pg. 76.

Factoring Review Jeopardy.

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

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:

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

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

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 +

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

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 -

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.

Special Factoring. Difference of Squares General Formula: (x) 2 – (y) 2 = (x + y)(x – y)

8.5 Factoring Differences of Squares (top)  Factor each term  Write one set of parentheses with the factors adding and one with the factors subtracting.

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.

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.

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

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

Polynomials and Polynomial Functions

Section 6.4: Factoring Polynomials

Chapter 6 Section 4.

4.5 & 4.6 Factoring Polynomials & Solving by Factoring

Factoring Special 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.

Algebra II with Trigonometry Mrs. Stacey

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

Factoring Perfect-Square Trinomials and Differences of Squares

Chapter 6 Section 3.

Chapter 6 Section 4.

Polynomials and Polynomial Functions

Special Factoring Formulas & a General Review of Factoring

Polynomials and Polynomial Functions

Factoring Perfect Square Trinomials and the Difference of Two Squares

Unit 5 Factor Special Products

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

Factoring Special Forms

FACTORING SUMS and DIFFERENCES of CUBES

Polynomials and Polynomial Functions

Chapter 6 Section 3.

5.5: Factoring the Sum and Difference of Two Cubes

Section 9.7 “Factor Special Products”

Sum/Diff Cubes and PST Brett Solberg AHS ‘11-’12.

Pre-Calculus Sec 1.3 Algebraic Expression

Algebra II with Trigonometry Mr. Agnew

Chapter 6 Section 3.

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)

F i v e o r m s o f a c t o r i n g.

Factoring Polynomials, Special Cases

Presentation transcript:

factoring special products Formulas to memorize! Section 6.3 factoring special products Formulas to memorize!

FORMULAS… Memorize these! Perfect Square Trinomials: a2 + 2ab + b2 = (a + b)2 Difference of 2 Squares: a2 - b2 = (a + b)(a – b) Difference of 2 Cubes: a3 – b3 = (a – b)(a2 + ab + b2) Sum of 2 Cubes: a3 + b3 = (a +b)(a2 - ab + b2)

EX: Factor 1. x3 – 8y3 2. x2 – 4x + 4 3. 4a2 – 25b4

EX: Factor some more! 4. m4 - 81 5. 27r3 + 8v3 6. 64 – (x – y)2

Guidelines for Factoring 1. Check for a GCF 2. 2 Terms: 2 Squares or 2 Cubes? Squares: if they are subtracted, use the difference of 2 squares formula. Cubes: use either the sum of 3 cubes formula or the difference of 2 cubes formula. 3. 3 Terms: Is it a perfect square? YES: use Perfect Square Trinomial formula NO: use REVERSE FOIL METHOD 4. 4 Terms: factor by GROUPING

Examples… factor each completely 1. x2 – 8x + 15 2. 9x2 + 30x + 25 3. 24a5y – 2a4y2 – 12x3y3 4. x2y + 3x – xy2 – 3y 5. 5m5 + 10m3n2 + 5mn4 6. (x + y)3 + (x – y)3