4.4 An Introduction to Factoring: The Greatest Common Factor; Factoring by Grouping Greatest Common Factor (GCF): the largest whole number that is a factor of each integer. Finding the GCF of Two or More Integers • Find the prime factorization of each integer by expressing each integer as the product of prime numbers. • Write the prime factors that are common to each integer; the GCF is the product of these prime factors. Example 1 Find the GCF of: a) 24, 30, 54 b) 48, 72, 84 Example 2 Finding the GCF of Two or More Variable Terms Find the GCF of 20x7 and 28x3 Factor the GCF out of each term of a polynomial Factor out the GCF from all of the terms Example 3 Factor 9x4 + 15x3 – 3x2 by factoring out the GCF. Factor out a common binomial factor from a polynomial Example 4 Factor 8x(7x – 2) – 5(7x – 2) by factoring out the GCF. Factoring by Grouping Factor a common factor out of the first two terms and another common factor out of the last two terms. If the two “groups” share a common binomial factor, factor out this binomial to complete the factoring of the polynomial. Example 5 Factor x3 + 4x2 + 7x + 28 Example 6 Factor x3 + 8x2 – 3x – 24 Example 7 Factor 5x2 + 35x – 10x – 70