8-4A Factoring Trinomials when the Leading Coefficient isn’t 1.

Slides:

Advertisements

Similar presentations

5.1 Rules for Exponents Review of Bases and Exponents Zero Exponents

Advertisements

Factoring Trinomials.

5-11 Using several methods to factor Objective to factor completely. Objective to factor completely. Guidelines: Guidelines: 1. Factor out the greatest.

Products and Factors of Polynomials

There is a pattern for factoring trinomials of this form, when c

8-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Multiplying Polynomials

Factoring Trinomials When a=1 ALWAYS check for GCF first! Factor trinomials in the standard form ax²+ bx + c Solve equations in the standard form ax²+

Factoring Trinomials.

13.1 Factoring Greatest Common Monomials with Algebra Tiles.

Factoring Polynomials

Factoring Quadratics — ax² + bx + c Topic

Digital Lessons on Factoring

LIAL HORNSBY SCHNEIDER

8-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz

Identifying Terms, Factors, and Coefficients

Do Now 3/3/10  Take out HW from last night. Text p. 578, #4-48 multiples of 4  Copy HW in your planner. Text p. 586, #4-52 multiples of 4  In your notebook,

Chapter 11 Polynomials.

8-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7.3 Factoring by Grouping CORD Math Mrs. Spitz Fall 2006.

Factoring ax2+bx +c ax2+bx +c

9-8 Completing the Square Warm Up Lesson Presentation Lesson Quiz

8-4B Solving Quadratic Equations when the Leading Coefficient isn’t 1.

4.7 Complete the Square.

Completing the Square Topic

Polynomials and Factoring

Polynomials Terms and Factoring Algebra I H.S. Created by: Buddy L. Anderson Algebra I H.S. Created by: Buddy L. Anderson.

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Objective Factor quadratic trinomials of the form x2 + bx + c.

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

Factoring Algebraic Expressions Multiplying a Polynomial by a Monomial Multiplying a Binomial by a Binomial Dividing a Polynomial by a Monomial Dividing.

Lesson 8-6 Warm-Up.

8-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

8-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Polynomials A monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents. The degree of a monomial.

Factoring Trinomials with a > 1 Factor trinomials when the coefficient of x 2 is a number greater than 1. ax 2 + bx + c.

Martin-Gay, Beginning Algebra, 5ed 22 Example Solution Think of FOIL in reverse. (x + )(x + ) We need 2 constant terms that have a product of 12 and a.

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

Aim: How do we multiply polynomials? Do Now: Multiply the following 1. 2x(3x + 1) 2. (x – 1)(x + 2) 3. (x +2)(x 2 – 3x + 1)

Algebra I Review of Factoring Polynomials

CLASSIFYING POLYNOMIALS. A _______________ is a sum or difference of terms. Polynomials have special names based on their _______ and the number of _______.

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

ALGEBRA 1 Lesson 8-2 Warm-Up. ALGEBRA 1 This is an area model using Algebra Tiles. Simply model 3x + 1 on the top (length of rectangle) and 2x on the.

Factor Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper.

Warm Up. y = 8x 2 – 16x -10 = roots a = 8, b = – 16, c = -10 Axis of symmetry = -b 2a x = -(-16) 2(8) = 1 y = 8(1) 2 – 16(1) -10 = -18 Vertex= minimum.

Factor Perfect Squares and Factoring Algebra 1 Glencoe McGraw-HillLinda Stamper.

Understanding Polynomials

Holt McDougal Algebra 1 Factoring x 2 + bx + c Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper.

Identifying Terms, Factors, and Coefficients (3.1.1) February 1st, 2016.

Chapter 5.1/5.2 Monomials and Polynomials. Vocabulary: A monomial is an expression that is a number, a variable, or the product of a number and one or.

8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper GMF is similar to GCF. Greatest Monomial Factor is similar.

Holt McDougal Algebra 1 Factoring x 2 + bx + c Factor quadratic trinomials of the form x 2 + bx + c. Objective.

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

MTH Algebra Factoring Trinomials of the form ax 2 + bx + c where a = 1 Chapter 5 Section 3.

Add and Subtract Polynomials Lesson 9.1 OBJ: to add and subtract polynomials.

Warm Up SUM-PRODUCT PUZZLES

Section 6.6 Solving Quadratic Equations Math in Our World.

7-6 Multiplying Polynomials Do you remember algebra tiles? Algebra 1 Glencoe McGraw-HillLinda Stamper.

8-3A Factoring Trinomials and Solving Quadratic Equations

Identifying Terms, Factors, and Coefficients (3.1.1)

Objective Factor quadratic trinomials of the form ax2 + bx + c.

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Algebra 1 Section 10.3.

Homework Help Ch 8-4.

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

There is a pattern for factoring trinomials of this form, when c

Presentation transcript:

8-4A Factoring Trinomials when the Leading Coefficient isn’t 1. X-Factor method Algebra 1 Glencoe McGraw-Hill Linda Stamper

Factoring quadratic trinomials means finding the binomial factors when given a product. The factors represent the length and width of the rectangle. You need to find the factors! You need to find the factors! x + 2 You are given the product – quadratic trinomial!

Multiply a times c to find the product. –3 All of the previous problems involving quadratic trinomials had a leading coefficient of 1. Multiply a times c to find the product. –3 –3 1 –2 b in the bottom represents the sum Check by doing FOIL in your head! You know there will be an x in each factor! You know there will be an x in each factor!

Today’s problems involve factoring quadratic trinomials when the leading coefficient isn’t 1 - this includes negative 1. To factor quadratic trinomials when the leading coefficient isn’t 1, you will use the X figure and then factor out the greatest monomial factor (aka greatest common factor).

Step 1 Use the X figure as you did when the leading coefficient was 1. –10 Multiply a times c to find the product. – 5 –5 + 2 2 –3 b in the bottom represents the sum Step 2 Take the coefficient “a” and the x from the ax2 term and the numbers from the sides of your X figure and place them into two parentheses in the following manner. ( )( ) Step 3 Factor out the greatest monomial factor from each parentheses if you can. Step 4 Discard the factor/s you pull out after X figure. Step 5 Check using FOIL.

–3 –10 2 – 5 –5 + 2 ( )( ) Check using FOIL. You must discard (X out) the GMF that is pulled out after using the X figure! ( )( ) Check using FOIL.

DO NOT DISCARD THIS FACTOR! Before you use the X figure, you must factor out any greatest monomial factor, if possible! You must keep the GMF that is pulled out before using the X figure! DO NOT DISCARD THIS FACTOR!

Factor. -10 - 5 -5 + 2 2 -3 ( )( ) If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it. Check using FOIL.

Factor out a GMF before the X figure – you must keep it! Factor out a GMF after the X figure – discard it (X it out)!

Try this problems... 5 –4 A polynomial that cannot be written as a product of two polynomials with integral coefficients is called a prime polynomial!

Copy all of the above problems before you start to factor! Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Copy all of the above problems before you start to factor!

Can you factor out a greatest monomial factor? Example 1 Factor. 6 + 3 3 + 2 2 5 Can you factor out a greatest monomial factor? ( )( ) Check using FOIL.

before using the X figure, keep it, Factor. Example 2 Example 3 -22 -18 + 22 22 - 1 -1 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? + 6 6 - 3 -3 21 3 ( )( ) ( )( ) Check using FOIL. If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

Factor. Example 4 Example 5 36 + 9 9 + 4 4 13 ( )( ) Check using FOIL. Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? 13 ( )( ) Check using FOIL.

Factor. Example 6 Example 7 280 -12 - 6 -6 + 2 2 -8 -35 -4 -43 Make an organized list of factors. 1•280 2•140 4 •70 5 •56 7 •40 8 •35 280 -12 - 6 -6 + 2 2 -8 -35 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? -4 -43 (10x - 8)(10x - 35) ( )( ) Check using FOIL. Check using FOIL.

Factor. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7

Homework 8-A9 Page 445-446 # 11–22,44,46-51.