Factorization Methods and Factor Tables in Mathematics

Explore the techniques of factorization through Tic-Tac-Toe method and factor tables. Learn how to find pairs of numbers that multiply to a given result, factor polynomials correctly, and understand the importance of factoring in mathematics concepts. Engage with visual representations and step-by-step explanations to enhance your factorization skills.

• Factorization
• Mathematics
• Tic-Tac-Toe
• Factor Tables
• Polynomials

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1. TIC-TAC-TOE FACTORING Presented by: Jennifer Morgan and Christina Guynes Grady ISD Kermit ISD

2. DAY ONE FACTOR TABLES Find the pair of numbers that will multiply to make the bottom number and add to give you the top number. 7 9 10 3 4 6 4 5 4 12 20 24

3. FACTOR TABLES -5 -25 40 -3 -8 -21 4 4 36 3 -4 -7 -24 84 144 -28

4. TIC-TAC-TOE METHOD 7 2 + + x x 2 3 2 3 6 1 1 2 3 Factors must multiply across to last number Multiply across to get this number Third term goes here What factors of 6 will add to get 7? First term goes here 1 Factors multiply up x to top number X s go in the first column Factors come from the diagonals 6 2 ( x + + 1 )( ) 3 x x

5. + + 2 3 16 5 n n Multiply across to get this number Third term goes here 3 5 15 1 1 3 5 n First term goes here What factors of 15 will add to get 16? 1 Factors multiply up n to top number n s go in the first column 15 Factors come from the diagonals Factors must multiply across to last number + ) 5 + 3 ( 1 )( n n

6. + x 2 3 7 10 x What factors of 30 will subtract to get 7? 3 -10 -30 1 1 x Does 3 go into 10 evenly? Which factor needs to be negative to get a positive 7? 10 10 3 - x No, so put a 1 in this place. 3 - x Negatives transfer to middle column + 3 ( 10 )( ) 1 x

7. x 2 4 4 15 x What factors of 60 will subtract to get 4? Start with the 4. It can t go into either 6 or 10 evenly, so we have to split it to 2 and 2. 4 -15 -60 2 2 5 Factors of 60 1 * 60 2 * 30 3 * 20 4 * 15 5 * 12 6 * 10 3 6 -10 x - x Negatives transfer to middle column + 2 ( 5 )( 2 ) 3 x x

8. + 2 9 17 8 x x What factors of 72 will add to get 17? 9 8 72 -8 9 1 Factors of 72 1 * 72 2 * 36 3 * 24 4 * 18 6 * 12 8 * 9 1 -8 -9 x - x ) 1 9 ( 8 )( x x

9. If the trinomial has a GCF, it needs to be removed first! + = + 2 2 4 18 8 2 ( 2 9 ) 4 x x x x What factors of 8 will add to get 9? 2 4 8 -1 1 2 4 ) 4 -1 x - -8 x Do NOT forget the 2 you pulled out at the beginning! 2 ( 2 1 )( x x

10. + 2 2 2 11 5 x xy y 2 5 10 1 1 2 5 ) 5 y - -1 x y - -10 x y 2 ( )( x y x Y s go in the second column

11. + 2 2 3 2 8 x xy y 3 -8 -24 - 3 2 Factors of 24 1 * 24 2 * 12 3 * 8 4 * 6 1 4 x -4 6 x y y + 3 ( 4 )( 2 ) x y x y

12. CONTACT INFORMATION Jennifer Morgan jennmorgan05@gmail.com Christina Guynes chguynes@kisd.esc18.net