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

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

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-2 5.1 – Factoring a Monomial from a Polynomial 5.2 – Factoring by Grouping 5.3 – Factoring Trinomials of the Form ax 2 + bx + c, a = 1 5.4 – Factoring Trinomials of the Form ax 2 + bx + c, a ≠ 1 5.5 – Special Factoring Formulas and a General Review of Factoring 5.6 – Solving Quadratic Equations Using Factoring 5.7 – Applications of Quadratic Equations Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3 Factoring a Monomial from a Polynomial

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4 Factors To factor an expression means to write the expression as a product of its factors. If a · b = c, then a and b are of c. a·bfactors Recall that the greatest common factor (GCF) of two or more numbers is the greatest number that will divide (without remainder) into all the numbers. Example: The GCF of 27 and 45 is 9.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5 Factors A prime number is an integer greater than 1 that has exactly two factors, 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 A composite number is an integer greater than 1 that is not prime. The first 15 composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25 The number 1 is neither prime nor composite.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6 Factors Prime factorization is used to write a number as a product of its primes. 48 = 2 · 2 · 2 · 2 · 3

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7 Determining the GCF 1.Write each number as a product of prime factors. 2.Determine the prime factors common to all the numbers. 3.Multiply the common factors found in step 2. The product of these factors is the GCF. Example: Determine the GCF of 48 and 60. 48 = 2 · 2 · 2 · 2 · 3 60 = 2 · 2 · 3 · 5 Two factors of 2 and a factor of 3 are common to both, therefore 2 · 2· 3 = 12 is the GCF.

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8 Determining the GCF To determine the GCF of two or more terms, take each factor the largest number of times it appears in all of the terms. Example: a.) Determine the GCF of the terms m 9, m 5, m 7, and m 4 The GDF is m 4 because m 4 is the largest factor common to all the terms.

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-9 Determining the GCF of Two or More Terms 1.Find the GCF of the numerical coefficients of the terms. 2.Find the largest power of each variable that is common to all of the terms. 3.The GCF is the product of the number from step 1 and the variable expressions from step 2. Example: Determine the GCF of 18y 2, 15y 3, 27y 5. The GCF of 18, 15, and 27 is 3. The GCF of y 2, y 3, and y 5 is y 2. Therefore, the GCF of the three terms is 3y 2.

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-10 Factoring Monomials from Polynomials 1.Determine the GCF of all the terms in the polynomial. 2.Write each term as the product of the GCF and its other factor. 3.Use the distributive property to factor out the GCF. Example: 6x + 18 (GCF is 6) = 6·x + 6·3 = 6 (x+ 3)