Algebra I B. MacDonald

 What is a GCF? What is a GCF?  Factoring out a GCF Factoring out a GCF

 Greatest Common Factor ◦ Largest number all values are divisible by ◦ The most variables the monomials have in common  If there isn’t a GCF, the polynomial is prime.  Example: 18x 3 + 9xy  Let’s try some The GCF would be 9x. Index Practice  Practice 

A. 30x 3 + 9x B. 12x x + 2 C. 16a 5 x 2 + 8a 3 x a 2 x D. 5x 2 + 4x + 2 3x 2 4a2x4a2x prime Index Helpful Hint CLICK HERE You made it. Return to the index for the next topic.

 Once you’ve factored out the GCF, write it in front, then write the leftovers inside parentheses.  GCF(leftovers) Practice  Practice  Index

A. 30x 3 + 9x B. 12x x + 2 C. 16a 5 x 2 + 8a 3 x a 2 x 3x 2 4a2x4a2x (10x 2 +3) (6x x + 1) (4a 3 x + 2ax 2 + 5) Checking our answer  Checking our answer  Index

 How can we check our factored answer? ◦ Distribute A. 30x 3 + 9x 3x(10x 2 +3) 30x 3 +9x YES!!! It works! How cool. I love math. Practice  Practice  Index

A. 12a a B. 15x + 25x 2 C. 12xy + 24xy 2 – 30x 2 y 4 GCF(leftovers) …. Check your answer too 4a(3a + 4) 5x(3 + 5x) 6xy(2 + 4y – 5xy 3 ) Index

 When factoring start with the smallest number, test the factors of that number.  Example: 12a 2 +16a + 20  Start with the factors of 12: 1, 2, 3, 4, 6, 12  What is the largest factor of 12 that both 16 and 20 are divisible by? 4  So the GCF is 4 (notice they all don’t have the variable a, therefore we can’t factor out a common variable) Return  Return 