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Mathematics Factoring Basics Guide

Start with simple multiplication, addition, and division facts. Learn how to find pairs of numbers that multiply and add up to specific values. Practice factoring quadratic equations step by step with examples.

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Mathematics Factoring Basics Guide

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  1. Welcome to Factoring Back to Basics Multiplication, Addition, Division

  2. Start with the simple stuff • What is 6 x 7? • 42 • What is 6 + 7 • 13 Very good

  3. More simple stuff • What is 3 x 5? • 15 • What is 3 + 5? • 8 See how simple!

  4. One more simple one • What is -3 x 4? • -12 • What is -3 + 4 • 1 Good job!

  5. Now lets go in reverse • What are 2 numbers that multiple to 10 and add to 7? • Start with finding all the multiples of 10 • 1 x 10, 2 x 5…… • Do any of those pairs also add up to 7? YES 5 and 2!

  6. Another one • Find 2 numbers that multiply to get 20 and add to get 9 • Multiples of 20? 1 x 20, 2 x 10, 4 x 5….. Any of those pairs add to get 9? 4 and 5

  7. One final one • Find 2 numbers that multiply to get -6 but add to get +1 • List all the multiples of -6 -1 X 6, 1 x -6, -2 x 3, -3 x 2… And the winner is…. -2 and 3

  8. Steps for Factoring • Is the quadratic in standard form? • List a, b, and c • Multiply a x c • Find all the multiples of • Find the pair that also adds to b • Make 2 sets of parentheses with an x in each one ( x )(x ) • Put your multiples of in each • Divide by a • Kick back

  9. Put it into practice Factor x² + 10x + 25 = 0 • 1 b. 10 c. 25 1 x 25 = 25 1 x 25, 5 x 5 Is it in standard form? List a. b. and c. Multiply a x c List the multiples of 25

  10. Continue x² + 10x + 25 = 0 5 and 5 (x ) (x ) (x + 5)(x + 5) DONE Which multiples also add to 10? Put 2 sets of parentheses with x’s in each Put your multiples in each Divide each multiple by a, if they divide nicely, leave alone

  11. Another example • 2x² + 9x + 10 = 0 a.2 b. 9 c. 10 2 x 10 = 20 1x20, 2x10, 4x5…… Is it in standard form? Find a. b. c. Multiply a x c List multiples of 20 Which set of multiples adds to 9?

  12. 4 + 5 = 9 (x )( x ) (x + 4)(x + 5) (x + 4)(x + 5) 2 2 (x + 2)(2x + 5) Put 2 sets of parentheses with x’s in each Put the multiples in each parentheses Divide each number by a Does 4 divide by 2? Does 5 divide by 2? Kickback

  13. Let’s practice • 2x² -7x + 5 = 0 a.2 b.-7 c. 5 2 x 5 = 10 -2 x -5 = 10 and -2 + -5 = -7 (x – 2) (x – 5) (x – 1)(2x – 5)

  14. Another?

  15. Answersto Day 1 Factoring Practice • (x + 5)(x +5) • (5x+2)(x+1) • (x – 8 )(x -3) • (x +4)(x+ 4) OR (x+4)² 5. (x – 1)(2x – 5)

  16. Answers 6. (x – 3)(5x-1) 7. (3x -3)(3x-3) OR (x-1)(x-1) 8. (x -4)(5x-1) 9. (4x + 10)(4x+10) OR (2x+5)(2x+5) 10. (x – 1)(6x -14) 11. (x+6)(3x+1) 12. (4x+10)(x+3)

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