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Working Backwards: Factoring Trinomials

Working Backwards: Factoring Trinomials. Method of Decomposition. Sometimes in math it helps to work backwards to solve a problem. With factoring trinomials this is called: method of Decomposition. Remember FOIL. Method of Decomposition relies on your knowledge of multiplying Binomials.

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Working Backwards: Factoring Trinomials

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  1. Working Backwards: Factoring Trinomials

  2. Method of Decomposition • Sometimes in math it helps to work backwards to solve a problem. • With factoring trinomials this is called: method of Decomposition.

  3. Remember FOIL • Method of Decomposition relies on your knowledge of multiplying Binomials. • If you have a good knowledge of how to use the concept of FOIL, then the method of composition should come easy to you. • F – first term • O – outside terms • I – inside terms • L – last terms

  4. Think about This x2 – 3x - 40 • When there is no number in front of the x2 we found factors using the following method: • Two numbers that multiply to give you the last term • 2) The same two numbers to give you the sum of the middle terms Therefore: Product of - 40 Sum of -3 (x – 8)(x + 5)

  5. Method of Decomposition Use this to decompose the trinomial When there is a number besides one in the front we do the follow: 8x2 + 10x + 3 You multiply the first constant by the last constant to get the product. 8x2 + 4x + 6x + 3 = (8x2 + 4x) + (6x + 3) = 4x(x + 1) + 3(x + 1) =(x + 1)(4x + 3) Product is + 24 8x2 + 10x + 3 +6 and +4 give the product of + 24 6x + 4x Which gives: 8x2 + 4x + 6x + 3

  6. Factor: 6y2 + 19y + 15 Solution: Think: What two integers have a product of +90 and a sum of +19. The numbers are +10 and +9 6y2 + 19y + 15 = 6y2+ 9y + 10y + 15 = (6y2 + 9y) + (10y + 15) = 3y(2y + 3) +5(2y + 3) = (2y + 3)(3y + 5) Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

  7. Factor: 2x2 – 7x - 15 Solution: Think: What two integers have a product of -30 and a sum of -7. The numbers are -10 and +3 2x2– 7x - 15 = 2x2-10x + 3x - 15 = (2x2 -10x) + (3x - 15) = 2x(x - 5) + 3(x - 5) = (2x +3)(x - 5) Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

  8. Factor: 9x2 + 15x + 4 You Try: Solution: Think: What two integers have a product of +36 and a sum of +15. The numbers are ? and ? 9x2+15x + 4 = = ( ) + ( ) = = Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

  9. Factor: 9x2 + 15x + 4 Answer: Solution: Think: What two integers have a product of +36 and a sum of +15. The numbers are +3 and +12 9x2+15x + 4 = 9x2+ 3x + 12x + 4 = (9x2 + 3x) + (12x + 4) = 3x(3x + 1) + 4(3x + 1) = (3x + 1)(3x + 4) Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

  10. Factor: 9x2 – 9x - 4 You Try: Solution: Think: What two integers have a product of +36 and a sum of -9. The numbers are ? and ? 9x2– 9x - 4 = = ( ) + ( ) = = Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

  11. Factor: 9x2 – 9x - 4 Answer: Solution: Think: What two integers have a product of -36 and a sum of -9. The numbers are -12 and + 3 9x2– 9x - 4 = 9x2-12x + 3x - 4 = (9x2 + 3x) + (-12x - 4) = 3x(3x + 1) -4(3x + 1) = (3x + 1)(3x – 4) Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

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