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8.5 Factoring Trinomials of the type x 2 + bx + c Objective: SWBAT solve a quadratic equation by factoring.

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Mini Quiz

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CAHSEE Review

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Overview Factoring x 2 + bx + c…(no GCF) Using the “X” Factor 4 Lines Factoring Reverse FOIL

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Factoring with the “X” Factor x 2 – x – 6 a = b = c = 1 -6 a·ca·c b + x (x + 2)(x – 3) Steps: 1.Draw your “X” 2.Fill in the a, b, c (ax 2 + bx + c) 3. Write the Factor 1 -6

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Factoring with the “X” Factor 1. x 2 – 5x x 2 – 6x x 2 – x 2 – 6x – 16 + x (x – 2) (x – 3) (x – 3) 2 (x + 4) (x – 4) (x – 8) (x + 2)

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4 Line Factoring Factor x 2 – x – 6 x 2 – x – 6 – x – 3x x+ 2 Steps: 1.Write the trinomial on top 2.Write the “b” term on the bottom 3.Think: “what two things multiply to the “a” term 4.Think: “What two things multiply to the “c” term 5.Cross multiply to check 2x2x -3x (x – 3) (x + 2)

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4 Line Factoring Factor 5. x 2 – 10x x 2 + 6x – x 2 + 4x x 2 – 4 (x – 5) (x + 9) (x – 3) (x + 2) 2 (x + 2) (x – 2)

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Factoring by Reverse FOIL Factor x 2 – x – 6 Steps: 1. Set up your ( )( ) 2. Guess factors for F 3. Guess factors for L 4. Check O and I ( )( )xx – x +2x = -x (x – 3)(x + 2)

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Factoring by Reverse FOIL Factor 9. x x x 2 – 17x x 2 – x 2 – 12x + 36 (x + 10)(x + 1) (x – 12)(x – 5) (x – 7)(x + 7) (x – 6) 2

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Wrap Up Factoring - “X” Factor - Using 4 lines method - Reverse FOIL HW: P. 397 #1-37 EOO; P. 407 #1-6 all; all Write DLUQ for notes + x ( )

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