Page 251 - Algebra 1

L E S S O N Simplifying Expressions Using the GCF 38
Warm Up
1. Vocabulary When two or more quantities are multiplied, each is a
(2)
Simplify.
2. 2x(3x - 5)
(term, factor) of the product.
(16)
3. -3x2y(4x2 - 7xy)
(16) _5
4. x
_-3 (32) x
1
5. -(-4)3
Simplifying expressions that contain numbers often requires knowledge of prime numbers and factors. Recall that a prime number is a whole number that is only divisible by itself and 1.
2 = 1 · 2 5 = 1 · 5 13 = 1 · 13 19 = 1 · 19
All whole numbers other than 1 that are not prime are composite numbers.
Composite numbers have whole-number factors other than 1 and the number itself. They can be written as a product of prime numbers, which is called the prime factorization of a number.
4=2·2 6=2·3 8=2·2·2
Several methods can be used to find the prime factorization of a number. The process requires breaking down the composite numbers until all the factors are prime numbers.
The prime factorization for the number 24 can be found in at least three ways.
(32)
New Concepts
Math Reasoning
Formulate Find all of the prime numbers that are less than 100.
24 = 2 · 12 =2·2·6
=2·2·2·3 2
24
2 24
2 12 3 2 6 3 3 1
4
6
2
2
Online Connection www.SaxonMathResources.com
It does not matter which method is used to find a prime factorization. The final product, however, must consist of only prime numbers. The factors are usually written in ascending order.
236 Saxon Algebra 1