Factoring Trinomials Continued

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Presentation transcript:

Factoring Trinomials Continued Method of Decomposition

Method of Decomposition Recall: Factoring Trinomials is working backwards from FOIL F – first term O – outside terms I – inside terms L – last terms (x-8)(x+5) F: (x)(x)=x2 O: (x)(5)=5x I: (-8)(x)= -8x L: (-8)(5)=-40 X2+ 5x - 8x - 40

Think about how you factor: You want two numbers that MULTIPLY to give you the last term The same two numbers ADD to give you the middle term (x-8)(x+5) F: (x)(x)=x2 O: (x)(5)=5x I: (-8)(x)= -8x L: (-8)(5)=-40 X2+ 5x - 8x – 40 X2 -3x - 40 Therefore: Product of - 40 Sum of -3 (x – 8)(x + 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(2x + 1) + 3(2x + 1) =(2x + 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

Factor: 6y2 + 19y + 15 6y2 + 19y + 15 = 6y2 + 9y + 10y + 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

Factor: 9x2 – 9x - 4 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

Factor: 9x2 – 9x - 4 9x2 – 9x - 4 = 9x2 -12x + 3x - 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

Factor: 5x2 + 8x - 4 5x2 +8x - 4 = = ( ) + ( ) You Try: Solution: Think: What two integers have a product of -20 and a sum of +8. The numbers are ? and ? 5x2 +8x - 4 = = ( ) + ( ) Group to factor Factor each bracket Collect common Factors Expand to check solution is correct

Try this: 4y2 - 16y + 7