Monomials and Factoring (GCF) (8-1) Objective: Factor monomials and find Greatest Common Factors.

Factor Monomials Factoring a monomial is similar to factoring a whole number. A monomial is in factored form when it is expressed as the product of prime numbers and variables, and no variable has an exponent greater than 1.

Example 1 Factor 18x2y3 completely. 2 ∙ 3 ∙ 3 ∙ x ∙ x ∙ y ∙ y ∙ y

Check Your Progress Choose the best answer for the following. Factor 15a3b2 completely. 15 ∙ a ∙ a ∙ a ∙ b ∙ b 3 ∙ 5 ∙ a ∙ a ∙ a ∙ b ∙ b 3 ∙ 5 ∙ a3b2 3 ∙ 5 ∙ a ∙ a ∙ a ∙ b2

Greatest Common Factor Two or more whole numbers may have some common prime factors. The product of the common prime factors is called the greatest common factor. The greatest common factor (GCF) is the greatest number that is a factor of both original numbers. The GCF of two or more monomials can be found in a similar way.

Example 2 Find the GCF of 27a2b and 15ab2c. 27a2b = 3 ∙ 3 ∙ 3 ∙ a ∙ a ∙ b 15ab2c = 3 ∙ 5 ∙ a ∙ b ∙ b ∙ c GCF = 3ab

Check Your Progress Choose the best answer for the following. Find the GCF of 39x2y3 and 26xy4. 2xy 13xy 39x2y3 13xy3 39x2y3 = 3 ∙ 13 ∙ x ∙ x ∙ y ∙ y ∙ y 26xy4 = 2 ∙ 13 ∙ x ∙ y ∙ y ∙ y ∙ y

Example 3 The lengths of the sides of a triangle are 12wz2, 8wz, and 16w2z. Find the GCF of the three lengths. 12wz2 = 2 ∙ 2 ∙ 3 ∙ w ∙ z ∙ z 8wz = 2 ∙ 2 ∙ 2 ∙ w ∙ z 16w2z = 2 ∙ 2 ∙ 2 ∙ 2 ∙ w ∙ w ∙ z GCF = 4wz

Check Your Progress Choose the best answer for the following. Mary is making bracelets with large and small beads. She has 20 large beads and 96 small beads. What is the greatest number of bracelets she can make without having any beads left over? 3 bracelets 4 bracelets 5 bracelets 8 bracelets 20 = 2 ∙ 2 ∙ 5 96 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3