Algebra 1 Section 10.3.

Slides:

Advertisements

Similar presentations

3.3 Homework Questions?.

Advertisements

AC Method of factoring ax2 + bx +c

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

Factoring Trinomials of the form

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

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

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

For Common Assessment Chapter 10 Review

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

Polynomial Review What is a polynomial? An algebraic expression consisting of one or more summed terms, each term consisting of a coefficient and one or.

Lesson 8-8 Warm-Up.

Objective 1.Factor quadratic trinomials of the form x2 + bx + c.

CHAPTER 8: FACTORING FACTOR (noun) –Any of two or more quantities which form a product when multiplied together. 12 can be rewritten as 3*4, where 3 and.

PATTERNS, ALGEBRA, AND FUNCTIONS

Factoring Trinomials. Recall by using the FOIL method that F O I L (x + 2)(x + 4) = x 2 + 4x + 2x + 8 = x 2 + 6x + 8 To factor x 2 + bx + c into (x +

Factoring Trinomials of the Form ax2 + bxy + cy2

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

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.4 Factoring Trinomials of the Form ax 2 + bx + c by Grouping.

CHAPTER 8.3 Objective One Factoring Polynomials in the form of ax 2 +bx+c using trial factors.

Factoring Trinomials with ax 2 + bx + c 6x x Now you need to find the right combination of numbers in the correct order.

Warm Up: Review Multiply the polynomials: 1. (x – 4)(2x – 2) 3. 3x(2x 2 y + 2xy + 3y + 4) 2. (3x – 1)(x + 3) 4. 2x(15x + 4) + 3(15x + 4)

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

Algebra I Notes Section 9.6 (A) Factoring ax 2 + bx + c With Leading Coefficient ≠ 1.

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)

REVIEW OF FACTORING Chapters 5.1 – 5.6. Factors Factors are numbers or variables that are multiplied in a multiplication problem. Factor an expression.

Chapter 11 Polynomials 11-1 Add & Subtract Polynomials.

Chapter 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Factoring.

Chapter 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Factoring.

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

Factoring – Day 4 Factoring Trinomials Objective: To factor trinomials whose quadratic coefficient is 1.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 5 Polynomials and Factoring.

Adding and Subtracting Polynomials Multiplying Polynomials Factoring Polynomials.

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

Chapter 9 Final Exam Review. Add Polynomials (2x² + x³ – 1) (2x² + x³ – 1) Like Terms terms that have the same variable (2x³ – 5x² + x) + (2x³ – 5x² +

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

Factoring Quadratic Trinomials a = 1 Chapter 10.5.

Warm Up SUM-PRODUCT PUZZLES

Factoring Quadratic Expressions Lesson 4-4 Part 1

Factoring Trinomials.

Unit 3.1 Rational Expressions, Equations, and Inequalities

Factor It’s a big deal!.

Factoring Polynomials

using the Diamond or "ac" method

§ 5.4 Factoring Trinomials.

Section R.4 Factoring.

Factoring Polynomials

Section 6.2 factoring trinomials.

Factoring trinomials ax² + bx +c a = 1

Factoring Trinomials A

Factoring Polynomials

Factoring Learning Resource Services

Polynomials and Polynomial Functions

Polynomials and Polynomial Functions

Factoring Polynomials

Warm Up Find each product. 1. (x – 2)(2x + 7) 2. (3y + 4)(2y + 9)

Algebra 1 Section 10.1.

Tonight : Quiz Factoring Solving Equations Pythagorean Theorem

Factoring Special Cases

Factor into pairs like in “T” Find the pair whose sum is “b”

Factor into pairs like in “T” Find the pair whose sum is “b”

Algebra 1 Section 10.2.

Factoring ax2 + bx + c CA 11.0.

The Greatest Common Factor

§ 6.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials.

Factoring Trinomials of the form ax2 + bx + c

Factoring Polynomials

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

Presentation transcript:

Algebra 1 Section 10.3

Factoring ax2 + bx + c (3x – 2)(x + 5) 3x2 + 15x – 2x – 10 Sum of the middle terms First terms (FOIL) Last terms (FOIL)

Find factors of +6 whose sum is +7. Example 1 Factor 3x2 + 7x + 2. ac = 6 and b = 7 Find factors of +6 whose sum is +7. 3x2 + 1x + 6x + 2

Example 1 3x2 + 1x + 6x + 2 Group the first two terms and the last two terms and factor the GCF from each grouping. (3x2 + 1x) + (6x + 2) x(3x + 1) + 2(3x + 1) (x + 2)(3x + 1)

Factoring Trinomials of the Form ax2 + bx + c Find factors of ac whose sum is b. Rewrite the middle term as a sum of terms with these factors of ac as their coefficients.

Factoring Trinomials of the Form ax2 + bx + c Factor the four-term polynomial by grouping the terms in pairs. Factor the common monomial from each pair. Factor the common binomial from each new term.

Factoring Trinomials of the Form ax2 + bx + c Check your factorization by multiplying the factors.

Example 2 Factor 2x2 – 19x + 24. ac = 48 and b = -19 Find factors of +48 whose sum is -19. Both factors must be negative. 2x2 – 3x – 16x + 24

Example 2 2x2 – 3x – 16x + 24 (2x2 – 3x) + (-16x + 24)

Find factors of -60 whose sum is -7. Example 3 Factor 3x2 – 20 – 7x. 3x2 – 7x – 20 ac = -60 and b = -7 Find factors of -60 whose sum is -7. 3x2 – 12x + 5x – 20

Example 3 3x2 – 12x + 5x – 20 (3x2 – 12x) + (5x – 20)

Factoring Remember: The first step in factoring a polynomial is to factor out any common monomial factors. In Example 4, there is a common factor of 2x.

Find factors of 30 whose sum is -13. Example 4 Factor 12x3 – 26x2 + 10x. 2x(6x2 – 13x + 5) ac = 30 and b = -13 Find factors of 30 whose sum is -13. 2x(6x2 – 10x – 3x + 5)

Example 4 2x(6x2 – 10x – 3x + 5) 2x[(6x2 – 10x) + (-3x + 5)]

Example 5 Factor 2x2 + 3xy – 14y2. Proceed as before, but remember the “y”. ac = -28 and b = 3 Find factors of -28 whose sum is 3. 2x2 + 7xy – 4xy – 14y2

Example 5 2x2 + 7xy – 4xy – 14y2 (2x2 + 7xy) + (-4xy – 14y2) x(2x + 7y) – 2y(2x + 7y) (x – 2y)(2x + 7y)

Factoring ax2 + bx + c It is also possible, for trinomials with small coefficients, to use a method of listing the combinations of coefficients. Notice that Example 6 uses this method, and notice the similarities to Example 5.

Homework: pp. 418-419