Factoring Introduction of GCF Algebra 1. Definition: GCF Factors are numbers that you can multiply together to result in another number. GREATEST COMMON.

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Presentation transcript:

Factoring Introduction of GCF Algebra 1

Definition: GCF Factors are numbers that you can multiply together to result in another number. GREATEST COMMON FACTOR The highest number that divides evenly into two or more numbers.

GCF: How To Prime Factorization Trial and Error (Division) 24 & 48

Examples… Let’s Start with Numbers! A) 30 and 40 B) 14 and 49 C) 15 and 75

What do we do with variables? The GCF with variables means that we can factor out the greatest number of variables that is common (or contained) in each term. Really, this means that we can only factor out the variable along with its smallest exponent. Let’s Break It Down… 3x 2 and 9x 4

Putting It All Together: “Undoing” the Distributive Property STEPS: 1)Find the GCF of the numbers. 2)Identify the GCF of the variables. 3)Write the GCF on the outside, open up your parenthesis, and work backwards with the distributive property to figure out what should go inside! 4)In other words, what would you have to multiply the GCF by to get the original terms back? What’s missing?

Examples Factor the Following Using the GCF! 1) 9b + 18b 2 2) 45x 2 – 25 3) 7ab – 35a 2 b

Examples 4) -3a 2 b + 6a 3 b 2 5) 20x 4 -30x-30 6) 4a 2 b 3 + 4a 2 b – 16a – 8

CHALLENGE Factor: 20x 8 y 2 z x 5 y 2 z + 35x 3 y 3 z You Create It! On your exit ticket, make your own polynomial that a classmate could use to practice factoring out a GCF. Also factor the polynomial that you’ve created on your own. We will use these questions as a warm up tomorrow!

End of Lesson Homework: 8.5 Worksheet