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