COLLEGE ALGEBRA 6.3. Factor by GCF Do Now: β’ Simplify the following statements 2π₯ π₯ + 4 8 π₯ β 4 + 2π₯ 2 Alsoβ¦ What is the greatest common factor of 9π₯ 2 π¦ and 12π₯π¦ 2 π§ Homework β’ Questions? β’ Comments? β’ Concerns? β’ Confusions? β’ ASK ASK ASK! Today: β’ We have been so focused on distributing things IN in order to simplify expressionsβ¦. What happens if we want to distribute OUT instead? Example One: β’ Factor Completely 16π β 8 Soβ¦. Always ask yourself, what can we take out? What do all the terms have in common? Example Two: β’ Factor Completely 32 β 56π You Try! β’ Factor Completely 3π₯ β 27 42 β 9π Example Three: β’ What happens when we add in some variables? Factor Completely 6π₯ 2 π¦ 3 + 2π₯ 5 Example Four: β’ Factor Completely 8π₯ 2 π¦ 4 β 16π₯ 5 π¦ 4 + 4π₯ 2 π¦ 3 Example Five: Factor Completely 3π4 π 8 π12 β 9π2 π 5 π 2 + 12π7 π 3 π Realize: Always start with the numbers. Then go to one variable, and then go to another variableβ¦. Donβt try to do it all at once! You will get overwhelmed and confused very quickly! Bottom Line: Go in a logical order! You Try! β’ Factor Completely 3π2 π 2 β 6π5 π 4 + 9π3 π 15π₯ 2 π¦ + 12π₯π¦ β 9π₯ 3 π¦ 5 *Realize: β’ Sometimes we may have some pieces that work, but not othersβ¦.. You need to find the common pieces for ALL terms, not just some! Example Six: β’ Factor Completely β48 + 24π + 56π 2 + 48π 3 Example Seven: β’ Factor Completely β25π₯ 2 π¦ 3 + 25π₯ 4 π¦ + 10π₯ 4 + 15π₯ 3 Example Eight: β’ Factor Completely 18π₯ 4 β π₯ 2 + 6π₯ 8 π¦ You Try! β’ Factor Completely 14π 3 + 21π + 49 12π2 π7 β 9ππ2 β 12ππ3 + 15π2 3ππ 3 β 6π3 π 4 + ab2 β 9a2 b3 Example Nine: β’ Slightly Trickierβ Factor Completely 66π4 π 8 π β π + 11π3 ππ + ππ Example Ten: β’ Factor Completely 6π₯ 3 π₯π¦ 2 + π¦ β 3π₯ π₯ 3 π¦ 3 β π₯ 2 π¦ Example Eleven: β’ Factor Completely 10π₯ 2 π¦ π2 π 3 β π5 π 2 + 30π₯ 3 π¦ 3 (π5 π + π 5 π) You Try! β’ Factor Completely β3π₯ 3 π¦ 8π₯π¦ 2 π§ β 1 + 2π₯ 3π₯π¦ 3 π§ β 9π₯ 2 π¦ 5 10π¦ 5π¦ 2 + 2π¦ β 3π¦ 3 β 10π¦ 4 3π₯ 3 2 β 5π₯ 2 + 2(9π₯ 3 β 3π₯ 5 ) Do Now: β’ Factor Completely 25π₯π¦π§ 2 + 10π¦ 2 π§ + 5π¦π§ 40π§ 3 π¦ + 32π§π₯ 3 + 40π§π₯π¦ + 48π§π₯ 28π₯ 6 π¦ 2 + 4π₯ 3 π¦ 2 β 24π₯ 3 π¦ 4 + 24π₯ 3 π¦ 3 β24π2 π 5 β 20ππ 3 β 16π2 + 16ππ Example Twelve: β’ Even Trickier: Factor Completely 3π + π2 2π2 β 1 + 2π4 π2 + 4π Example Thirteen: β’ Factor Completely π₯ 2 β 5π₯ 2π¦ 3 + π¦ 2 β π₯π¦ 2 You Try! β’ Factor Completely 8π₯ π₯π¦ 3 + π¦ 2 + 3π₯π¦ β π¦ 2π₯ 2 + π₯π¦ Example Fourteen: β’ Find two numbersβ¦. β’ A) Whose sum is 8 and whose product is 12 β’ B) Whose sum is 15 and whose product is 36 β’ C) Whose sum is -8 and whose product is 16 β’ D) Whose sum is -17 and whose product is 30 Example Fifteen: β’ Find two numbersβ¦. β’ A) Whose sum is 2 and whose product is -63 β’ B) Whose sum is -4 and whose product is -32 β’ C) Whose sum is -7 and whose product is -60 You Try! β’ Find two numbersβ¦ β’ A) Whose sum is 17 and whose product is 70 β’ B) Whose sum is 5 and whose product is -24 β’ C) Whose sum is -2 and whose product is -24 β’ D) Whose sum is -30 and whose product is 81 Practice Problems β’ Try some on your own/in your table groups β’ As always donβt hesitate to ask me questions if you are confused OR talk to a tablemateβ they are your greatest resource!
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