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Factoring Trinomials When a 1

Factoring Trinomials When a 1. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms. 1. GCF 2 or more 2. Diff. Of Squares 2 Trinomials 3 Grouping 4. Review: (3y + 2)(y + 4) Multiply using FOIL. FOIL:

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Factoring Trinomials When a 1

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  1. Factoring Trinomials When a 1

  2. Factoring ChartThis chart will help you to determine which method of factoring to use.TypeNumber of Terms 1. GCF 2 or more 2. Diff. Of Squares 2 • Trinomials 3 • Grouping 4

  3. Review: (3y + 2)(y + 4)Multiply using FOIL. FOIL: Combine like terms. 3y² + 12y + 2y + 8 = 3y² + 14y + 8 y² + (12 + 2)y + (2)(12) How would you get 24 from the 2nd step? *You need the factors of ac that add to = b.

  4. ax2 + bx + c * If p and q are factors of ac that add to = b and p > q. ax2 + bx + c ax2 - bx + c (x+p)(x+q) (x-p)(x-q) ax2 + bx – c ax2 – bx - c (x+p)(x-q) (x-p)(x+q)

  5. 1) Factor. 3y2 + 14y + 8Create a table as shown below. Factors of ac: Multiply the 1st and last coefficients: 3(8) = 24 Sum of b: Middle coefficient: 14 Factors of +24 Sum of +14 1, 24 2, 12 2 + 12 = 14* 3, 8 4, 6

  6. ( x + 12) (x + 2) now divide or reduce 12 and 2 by your a (a= 3) Factor. 3y2 + 14y + 8 ___ ___ 3 3 ( x + 12) (x + 2)*After you reduce, if there is a numberleft in the denominator,you take it to the front of the factor.

  7. ___ ___ ( x + 12) (x + 2) 3 3 = ( x + 4) (3x + 2) y

  8. 2) Factor. 5x2 - 17x + 14 • Factors of: Multiply the 1st and • last coefficients. • Sum of: Middle Term • Factors of +70 Sum of -17

  9. Factor. 5x2 - 17x + 14 Factors of +70 Sum of -17 -10, -7 -10 + -7 + -17 ( x - 10) (x – 7) now reduce 10 and 7 by your a (a= 5)

  10. ( x - 10) (x – 7)*After you reduce, if there is a numberleft in the denominator,you take it to the front of the factor. ___ ___ 5 5 =( x - 2) (5x – 7)

  11. FACTORING QUIZ

  12. It is not the easiest of things to do, but the more problems you do, the easier it gets! Trust me! 3) Factor. 2x2 + 9x + 10 (2x + 5)(x + 2)

  13. 12y2 - 26y – 10 • ****Do not forget** • 1st Step: Check to Factor GCF • GCF: 2 • 2( 6y2 - 13y – 5)

  14. 2( 6y2 - 13y – 5) Now we need to find the factors of ac that + to = b Factors of ac: a=6 and c = -5 so ac = -30. Sum of b: -13

  15. 2( 6y2 - 13y – 5) Factors of -30 Sum of -13 1, -30 2, -15 2 + -15 = -13 3, -10 5, -6

  16. Now reduce by the a term (a = 6)2(y + 2)(y – 15) ___ ___ 6 6 2 ( y + 1)( y – 5) ___ ___ 3 2 2(2y-5)(3y+1)

  17. 5) -12x2 - 11x + 5 -(3x-1)(4x+5) 6) 5x - 6 + x2 1st reorder: x2 + 5x - 6 (x-1)(x+6)

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