Factoring A Quadratic Expression Feb. 25, 2014. SWBAT Factor a Quadratic Expression WARM – UP 6x 6 – 4x 2 + 2x 12x 2 y + 24xy 2 – 28xy.

Slides:

Advertisements

Similar presentations

CLOSE Please YOUR LAPTOPS, and get out your note-taking materials.

Advertisements

2.2 – Factoring Polynomials Common Factoring. Whenever we are asked to factor the first thing that we should do is look for common factors. The Greatest.

Ch. 5 Polynomials, Polynomial Functions, & Factoring

MTH 091 Section 11.1 The Greatest Common Factor; Factor By Grouping.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.1 – Slide 1.

The Greatest Common Factor and Factoring by Grouping

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Section 5.1 Polynomials Addition And Subtraction.

Objectives The student will be able to: 7A: Find the prime factorization of a number, the greatest common factor (GCF) for a set of monomials and 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.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 6.1 Removing a Common Factor.

Recall: By the distributive property, we have x ( x + 2 ) = x² + 2x Now we’re given a polynomial expression and we want to perform the “opposite” of the.

5-4 Factoring Quadratic Expressions Objectives: Factor a difference of squares. Factor quadratics in the form Factor out the GCF. Factor quadratics with.

Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, , 55 GCF = 3 GCF.

GCF What does it stand for? What is it?. What do these have in common??

Factoring Polynomials: Part 1

Simple Factoring Objective: Find the greatest common factor in and factor polynomials.

Factoring using GCF interpret parts of an expressions such as terms, factors, and coefficient.

2.3 Factor and Solve Polynomial Expressions Pg. 76.

Addition and Subtraction of Polynomials.  A Polynomial is an expression comprised of one or more terms. Terms are separated by + or – (Polynomials are.

Factoring Polynomials: Part 1 GREATEST COMMON FACTOR (GCF) is the product of all prime factors that are shared by all terms and the smallest exponent of.

Factor the following special cases

Chapter 5 Section 4 Factoring Quadratic Expressions.

Polynomials Polynomials  Examples : Monomials: 4f 3x 3 4g 2 2 Binomials: 4t – 7g 5x 2 + 7x 6x 3 – 8x Trinomials: x 2 + 2x + 3 5x 2 – 6x.

Factoring – Greatest Common Factor When factoring out the greatest common factor (GCF), determine the common factor by looking at the following: 1.Numerical.

Adding and Subtracting Polynomials Multiplying Polynomials Factoring Polynomials.

DO NOW 11/12/14 Homework in the basket please Multiply the following polynomials 1. (3x + 1)(3x – 1) 1. (2z – 7)(z + 4) 1. (4a + 2)(6a2 – a + 2) 1. (7r.

Section 6.1 Factoring Polynomials; Greatest Common Factor Factor By Grouping.

Factoring Quadratic Expressions ax 2 + bx + c “SPLITTING THE MIDDLE” Feb. 27, 2014.

Factors are numbers you can multiply together to get another number Example: 2 and 3 are factors of 6, because 2 × 3 = 6 Objectives: SWBAT 1) find the.

Holt Algebra Dividing Polynomials Warm Up Divide. 1. m 2 n ÷ mn x 3 y 2 ÷ 6xy 3. (3a + 6a 2 ) ÷ 3a 2 b Factor each expression. 4. 5x x.

Factoring Polynomials. Part 1 The Greatest Common Factor.

8.2: Multiplying and Factoring. Warm-up:  Greatest Common Factor (GCF)  The greatest factor that divides evenly into each term of an expression  Find.

Factoring Greatest Common Factor. Factoring We are going to start factoring today. I will take it easy on you in the beginning. Factoring is one skill.

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

Topic: Factoring MI: Finding GCF (Greatest Common Factor)

Warm-up Given the functions, perform the following operations:

1-5 B Factoring Using the Distributive Property

8-5 Factoring Using the distributive property

Warm-up Find the GCF for the following: 36, 63, 27 6x2, 24x

Warm up Factor the expression.

Factoring Quadratic Expressions ax2 + bx + c

Lesson 6.1 Factoring by Greatest Common Factor

Objectives The student will be able to:

8-1 Adding and Subtracting Polynomials

Lesson 10.4B : Factoring out GCMF

Warm Up Find the GCF of each set of numbers and , 45 and 30

Chapter 5 – Quadratic Functions and Factoring

THE DISTRIBUTIVE PROPERTY: Factoring the Expression

Objective Factor polynomials by using the greatest common factor.

Factoring Quadratic Expressions

What is Factoring? Breaking apart a polynomial into the expressions that were MULTIPLIED to create it. If a Polynomial can not be factored, it is called.

Warm Up 1. 2(w + 1) 2. 3x(x2 – 4) 2w + 2 3x3 – 12x 3. 4h2 and 6h 2h

14 Factoring and Applications.

Factoring GCF and Trinomials.

Factoring Polynomials

Warm-up: Write in scientific notation: ,490,000

6.1 & 6.2 Greatest Common Factor and Factoring by Grouping

Factoring Using the Distributive Property

The Greatest Common Factor and Factoring by Grouping

Objective Factor polynomials by using the greatest common factor.

3.4 Solve by Factoring (Part 1)

Factoring – Greatest Common Factor (GCF)

Factoring Polynomials

Chapter Six FACTORING!.

Chapter Six FACTORING!.

Warm-up Find the GCF for the following: 36, 63, 27 6x2, 24x

Presentation transcript:

Factoring A Quadratic Expression Feb. 25, 2014

SWBAT Factor a Quadratic Expression WARM – UP 6x 6 – 4x 2 + 2x 12x 2 y + 24xy 2 – 28xy

SWBAT Factor a Quadratic Expression Greatest Common Factor (GCF) The Greatest Common Factor (GCF) is the largest numeric value and variable power that can be divided out of a polynomial. Always start by factoring out any GCF!

Example 1: Factor 8x 4 – 12x 3 – 16x 2 GCF: 4x 2 You can treat the coefficients separately from each variable. First, look for the largest value that is a factor of 8, 12, and is the largest value Then, for each variable, find the greatest power of that variable that can be divided out of that variable. The greatest power of x that can be divided out of x 4, x 3, and x 2 is x 2. SWBAT Factor a Quadratic Expression

Think of what will remain when you divide each term by the GCF. Writing the problem this way may help you see what the remaining factor is. **Recall that when you divide powers of a variable, you subtract the exponents. Write the GCF on the left, and the remaining factor in parentheses on the right. 4x 2 (2x 2 – 3x – 4)

SWBAT Factor a Quadratic Expression Example 2: 16x 4 – 12x 3 – 4x 2 Be Careful of This!!! GCF: 4x 2 4x 2 (4x 2 – 3x – 1)

SWBAT Factor a Quadratic Expression Practice 1: Factor each of these by determining the GCF 1.12ab + 30ac 2. p + prt 3.12x 2 y 3 – 18xy b 2 – 36b 3 5. x 3 – 3x 2 + x 6. 2x 4 – 6x x 6

SWBAT Factor a Quadratic Expression Example 2: Factor by Grouping When a polynomial has four terms, make two groups and factor out the GCF from each group. Factor 8x 3 + 6x x + 15 Step 1: Group terms that have common factors 8x 3 + 6x x + 15 Step 2: Identify and factor the GCF out of each group 2x 2 (4x + 3) + 5 (4x + 3)

SWBAT Factor a Quadratic Expression Step 3: Factor out the common binomial factor & Regroup: (4x + 3)(2x 2 + 5) Step 4: CHECK (4x + 3)(2x 2 + 5) = 8x 3 + 6x x + 15

SWBAT Factor a Quadratic Expression Factor each polynomial filling in the blanks x x a a 2 + 6

SWBAT Factor a Quadratic Expression Factor each polynomial by grouping x 2 (7x + 4) + 2(7x + 4) (3x 2 + 2)(7x + 4) 10x 2 (4x – 5) + 3(4x – 5) (10x 2 + 3)(4x – 5)

SWBAT Factor a Quadratic Expression SUMMARY HW P 14/ 1-20

SWBAT Factor a Quadratic Expression 1.3x x 2 + 9x 2. x 2 y 3 + xy 3. 4y 5 – 8y 4 -2y 2 4. A2T Apps: Greatest Common Factor Factoring EXIT TICKET QUIZ: Factor each of the following by GCF.