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FACTORING!!!

FACTORING!!!. Why? Review binomial multiplication. (X+3)(X+1). 1X 2. +1X. +3X. +3. +3. 1X 2. +4X. + C. A X 2. + B X. C= 3. A= 1. B= 4. X 2 +5X+6. A=1 •B=5 •C=6. The MAGIC Number : AC = 1•6 = 6. Now, list the factors of 6 .

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FACTORING!!!

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  1. FACTORING!!!

  2. Why? Review binomial multiplication (X+3)(X+1) 1X2 +1X +3X +3 +3 1X2 +4X +C AX2 +BX C=3 A=1 B=4

  3. X2+5X+6 • A=1 •B=5 •C=6 The MAGIC Number: AC = 1•6 = 6 Now, list the factors of 6. Now, which pair will get you to a sum of 5? 1,6 2,3 -1+6=5 +2+3=5 Both numbers in the sum need to be positive. Why?

  4. 5X X2+5X+6 X2+ 2X+3X+6 (X2+2X)+(3X+6) X(X+2)+3(X+2) (X+3)(X+2) 2X+3X FACTOR BY GROUPING!!! X 3 +

  5. X2-6X+5 • A=1 •B=-6 •C=5 The MAGIC Number: AC = 1•5 = 5 Now, list the factors of 5. Now, which pair will get you to a sum of -6? 1,5 -1+-5=-6 Both numbers in the sum need to be negative. Why?

  6. 6X X2- X +5 X2+-X+-5X+5 (X2+-X)+(-5X+5) X(X-1)-5(X-1) (X+3) (X-1) -X+-5X FACTOR BY GROUPING!!! -5 X

  7. 5X2+X-6 • A=5 •B=1 •C=-6 The MAGIC Number: AC = 5•-6 = -30 Now, list the factors of -30. Now, which pair will get you to a sum of +1? because it’s -30, one of the factors needs to be negative 1,-30 -1,30 3,-10 -3,10 6+-5=+1 2,-15 -2,15 5,-6 -5,6 The smaller number needs to be negative. Why?

  8. X 5X2+ X -6 5X2+6X+-5X -6 (5X2+6X)+(-5X-6) X(5X+6)-1(5X+6) (X-1)(5X+6) 6X+-5X FACTOR BY GROUPING!!! -1 X

  9. 7X2-4X-3 • A=7 •B=-4 •C=-3 The MAGIC Number: AC = 7• -3 = -21 Now, list the factors of -21. Now, which pair will get you to a sum of -4? because it’s NEGATIVE 21, one of the factors needs to be negative 1,-21 -1,21 3,-7 -3,7 -7+3=-4 The bigger number needs to be negative. Why?

  10. -4X 7X2-4X-3 7X2 -7X+3X -3 (7X2-7X)+(3X-3) 7X(X-1)+3(X-1) (7X+3)(X-1) -7X+3X FACTOR BY GROUPING!!! +3 7X

  11. X2-6X+9 • A=1 •B=-6 •C=9 The MAGIC Number: AC = 1• 9 = 9 Now, list the factors of 9. Now, which pair will get you to a sum of -6? 1,9 3,3 -3+-3=-6 Both numbers need to be negative. Why?

  12. -6X X2-6X+9 X2 -3X-3X +9 (X2-3X)+(-3X+9) X(X-1)-3(X-1) (7X+3)(X-1) -3X-3X FACTOR BY GROUPING!!! X -3

  13. X2-25 • A=1 •B=0 •C=-25 The MAGIC Number: AC = 1• -25 = -25 Now, list the factors of -25. Now, which pair will get you to a sum of 0? because it’s NEGATIVE 25, one of the factors needs to be negative 1,-25 -1,25 -5,5 -5+5=0 One of the numbers need to be negative. Why?

  14. X2-25 X2 -5x+5x -25 (X2-5X)+(5X-25) X(X-5)-5(X-5) (7X+3)(X-5) -5X+5X FACTOR BY GROUPING!!! X -5

  15. 4X2-49 • A=4 •B=0 •C=-49 The MAGIC Number: AC = 4• -49 = -196 Now, list the factors of -196. Now, which pair will get you to a sum of 0? because it’s NEGATIVE 196, one of the factors needs to be negative 1,-196 -1,196 4,-49 -4,49 14,-14 -14+14=0 2,-98 -2,98 7,-28 -7,28 One of the numbers need to be negative. Why?

  16. 4X2-49 4X2 -14x +14x -49 (X2-14X)+(14X-49) 2X(2X-7)+7(2X-7) (7X+3)(2X-7) -14X+14X FACTOR BY GROUPING!!! 2X +7

  17. 9X2+4 Try this one. Why can’t this be factored?

  18. X2+7X-6 Try this one. Why can’t this be factored?

  19. The small print Created by BaileeRosenvall. Please feel free to use and/or modify to suit your needs however, I ask that you do not remove my name from this creation. Thank you. June 10, 2010.

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