Week 1- MATH114N Exploring Factors and Factoring Trinomials

WEEK 1: Exploring Factors and Factoring Trinomials Factoring To factor a number means to write it as the product of 2 or more numbers. The product is the factored form of the number. Example: 14 =7 X 2 7 & 2 are the Factors. Together 7 & 2 make up the Factored form. **Factoring is a process that “undoes” multiplying. GREASTEST COMMON FACTOR What is a greatest common factor and how can we find it? The GCF is the highest number that divides exactly into two or more numbers. When we find all the factors of two or more numbers, some of the factors are the same (or “common”). For example: - 6 is a common factor of 18 and 24 because 6 factors in to both 18 and 24. Some other common factors of 18 and 24 are: 1, 2, and 3. **The GREATEST COMMON FACTOR of a list of integers is the LARGEST or HIGHEST common factor of those integers. In this example above: - The Greatest Common Factor would be 6. Find the Greatest Common Factor of a list of variable terms : Example: *The terms x^4, x^5, x^6, and x^7 have x^4 as the greatest common factor because the least exponent on the variable (x) in the factored forms is 4 : x^4=1*x^4, x^5=x*x^4, x^6= x^2*x^4, x^7=x^3*x^4 GCF= x^4 ** The exponent on a variable in the GCF is the least exponent that appears on that variable in ALL the terms, as shown above. Steps to find the Greatest Common Factor 1. Factor - Write each number in their prime factoring form ....................................CONTINUED..............................................