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# Factoring polynomials

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### Factoring polynomials

1. 1. Factoring Polynomials<br />Ann Georgy and Tiffany Kwok<br />Period 6<br />
2. 2. Doriβs list on how to factor<br />Polynomial<br />LOOK FOR A GCF or GMF!<br />Factor as product of Binomials<br />Not Factorable<br />Special Product<br />Factor of Grouping<br />Difference of Squares <br />PST<br />
3. 3. How to find GMF<br />Example:5π₯3and 10π₯2<br />Β <br />So the GMF isβ¦<br />You can figure out the GMF by writing it out, using Prime Factorization<br />=5Γπ₯Β Γπ₯Β Γπ₯<br />Β <br />=2Γ5Γπ₯Γπ₯<br />Β <br />GππΉ=5π₯2<br />Β <br />
4. 4. Factoring Polynomials<br />Like always find the GMF first. In this case the GMF is 4π₯3<br />Β <br />Next, divide each term by the GMF. SO that way each term will be the product of the GCF.<br />Example:8π₯4βΒ 12π₯3<br />Β <br />GMF: 4π₯3<br />Β <br />8π₯44π₯3β12π₯34π₯3Β <br />Β <br />=4π₯3(2π₯β3)<br />Β <br />The 8π₯4Β became 2π₯Β and 12π₯3became 3 after being divided by 4π₯3<br />Β <br />
5. 5. What do these to group have in common?<br />Use FOIL to double check your work<br />Before you do anything, group monomials that have a GCF.<br />Look they both have(π₯3β1)so now all you have to do is factor it out!<br />Β <br />Factor by Grouping<br />Example: 15π₯4β15π₯+12π₯3β12<br />Β <br />(15π₯4β15π₯)+(12π₯3β12)<br />Β <br />15π₯(π₯3β1)+12(π₯3β1)<br />Β <br />(π₯3β1)(15π₯+12)<br />Β <br />π₯3β115π₯+12=15π₯4β15π₯+12π₯3β12<br />Β <br />
6. 6. What if they are opposites?<br />Example: 5π₯2β10π₯+6π₯β3π₯2<br />Β <br />Like before, group the terms the monomials that have something in common.<br />Find the GMF of each group!<br />Oh my! Look (x-2) and (2-x) are two different things. So they donβt have a common factor? <br />NO! Actually they do, multiply (2-x) by -1 to change it around!<br />Now factor it out, and use FOIL to double check your work!<br />(-2+x) is the same as (x-2).<br />(5π₯2β10π₯)+(6π₯β3π₯2)<br />Β <br />5π₯(π₯β2)+3π₯(2βπ₯)<br />Β <br />5π₯(π₯β2)+3π₯(β1)(2βπ₯)<br />5π₯π₯β2β3π₯β2+π₯<br />5π₯π₯β2β3π₯(π₯β2)<br />(π₯β2)(5π₯β3)<br />Β <br />(π₯β2)(5π₯β3)= 5π₯2β10π₯+6π₯β3π₯2<br />Β <br />
7. 7. Factoring Binomails: π₯2+ππ₯+π<br />Β <br />You must find a pair of number, when added equals to B and gives a product of C.<br />(π₯,π¦)<br />Β <br />π‘π€=π<br />Β <br />π‘<br />Β <br />π€<br />Β <br />t+w=b<br />Β <br />
8. 8. Product of Binomials: π₯2+ππ₯+π<br />Β <br />What are some factors of 20 that add up to 9?<br />Look, the group (4,5) add up to 9 and have a product of 20.<br />The first term is π₯2Β , so thatβs why the variables need to have a coefficient of 1. Or (π₯+β)Β (π₯+β)<br />Β <br />Use FOIL to double check you work!<br />Example:π₯2+9π₯+20<br />20=1,20,Β 2,10,Β 4,5<br />Β <br />(π₯+4)(π₯+5)<br />Β <br />(π₯+4)(π₯+5)=π₯2+9π₯+20<br />Β <br />
9. 9. What if π is negative?<br />Β <br />It looks like the pair (2,-16) satisfies both these requirements!<br />Well, this is almost the same, what pair of numbers gives a product a -32, and a sum of -14?<br />Like before because π₯2Β  is the first term, the variable terms need to have a coefficient of 1.<br />Β <br />Use FOIL to double check you work!<br />Example:π₯2β14xβ32<br />Β <br />β32=β1,32,Β 2,β16,Β 4,β8,Β β32,1,Β (β2,16)Β <br />Β <br />(π₯+2)(π₯β16)<br />Β <br />(π₯+2)(π₯β16)= π₯2β14xβ32<br />Β <br />
10. 10. Product of Binomials: ππ₯2+π+π<br />Β <br />Use the FOIL method, to double check if it works!<br />Hey letβs try the pair (2,5), and see if it works. Remember to use the form (x+β) (x+β)!<br />Β <br />Look here a=3, b=12 and c=10. Try to find a pair of numbers in which there sum is 12 and product is 10. Well this is just guess and check!<br />Split upΒ 3π₯2 ! <br />Β <br />Example: 3π₯2+12x+10<br />Β <br />10=1,10,Β (2,5)<br />Β <br />(2π₯+2)(π₯+5)<br />Β <br />2π₯+2π₯+5=<br />3π₯2+12x+10<br />Β <br />
11. 11. Perfect Square Trinomial<br />In this case the pair is (-14,-14). Letβs try it out.<br />Use FOIL to see if it works.<br />Yes thatβs right, it is equal to(π₯β14)2! <br />Β <br />A Perfect Square Trinomial is when you square a binomial quantity. <br />Example: π₯2β28π₯+196Β <br />Β <br />Like before find a pair of numbers that has a sum of -28 and a product of 196<br />IT WORKS! But do you notice that (x-14) and (x-14) is the same? So that means it is equivalent to β¦<br />(π₯β14)(π₯β14)<br />Β <br />(π₯β14)(π₯β14)=π₯2β14π₯β14π₯+196Β <br />Β <br />(π₯β14)2<br />Β <br />
12. 12. Difference of Squares<br />The -56π₯2π¦ cancels out 56π₯2π¦ leaving us with 64π₯4β49π¦2<br />Β <br />Factor out the two monomials!<br />Use FOIL to double check your work!<br />A difference of Square's is when a square number is subtracted from another square number.<br />Example: 64π₯4β49π¦2<br />Β <br />(8π₯2+7y)(Β 8π₯2β7y)<br />Β <br />(8π₯2+7y)Β 8π₯2β7y=64π₯4β56π₯2π¦+56π₯2π¦β49π¦2<br />Β <br />(8π₯2+7y)(Β 8π₯2β7y)<br />Β <br />