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# Notes 10: X-Box Factoring Aim: Students will be able to factor a trinomial where a is greater than 1. ax 2 + bx + c HW #15: Red text p. 218 #s 1 – 7, and.

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Notes 10: X-Box Factoring Aim: Students will be able to factor a trinomial where a is greater than 1. ax 2 + bx + c HW #15: Red text p. 218 #s 1 – 7, and p. 222 #s 1-15 (1 st column)

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Directions: 1.Cut along the dotted lines. 2.Glue 2 of the x-box charts on page 33 and 34. 3.Title page 33: Notes: X-Box Factoring where a > 1 HW #15: Red text p. 218 #s 1 – 7, and p. 222 #s 1-15 (1 st column) Study for your quiz. *Some trinomial is not factorable, therefore it is prime.

1. FACTOR ____________________________ Last term 1 st Term Factor b acac __________________ = __________________ 3x 2 + 2x – 8 3(-8) = -24 +2 Since the product is negative, the factors must have different signs 3x 2 -8 + − Since b is positive, the larger factor must be positive What are factors of 24 that will give you 2? 64 = +2 +6x -4x Place the factors: 6 & -4 in the box and add an x to each x 3x Factors 3x, x +2 -4 (x + 2 )(3x – 4) Create your x-box x times ? = -4x 3x times ? = 6x What factors does 3x 2 & 6x have in common? 3x Page 33

2. FACTOR ____________________________ Last term 1 st Term Factor b acac __________________ = __________________ 5x 2 – 12x + 4 5(4) = 20 -12 Since the product is positive, the factors must have same signs as b 5x 2 +4 − − What are factors of 20 that will give you 12? 102 = -12 -2x -10x Place the factors: 6 & -4 in the box and add an x to each 5x x Factors 5x, x -2 (x – 2)(5x – 2) Create your x-box 5x times ? = -10x x times ? = -2x What factors does 5x 2 & - 2x have in common? x Page 33

3. FACTOR ____________________________ Last term 1 st Term Factor b acac __________________ = __________________ 2x 2 – 9x – 18 2(-18) = -36 -9 Since the product is negative, the factors must have different signs 2x 2 -18 + − Since b is negative, the larger factor must be negative What are factors of 36 that will give you 9? 312 = -9 +3x -12x Place the factors: 3 & -12 in the box and add an x to each 2x x Factors 2x, x +3 -6 (x – 6)(2x + 3) Create your x-box 2x times ? = -12x x times ? = 3x What factors does 2x 2 & 3x have in common? x Page 34

4. FACTOR ____________________________ Last term 1 st Term Factor b acac __________________ = __________________ 2x 2 – 9x + 10 2(10) = 20 -9 Since the product is positive, the factors must have same signs as b 2x 2 +10 - − What are factors of 20 that will give you 9? 45 = -9 -5x -4x Place the factors: -4 & -5 in the box and add an x to each 2x x Factors 2x, x -5 -2 (x – 2)(2x – 5) Create your x-box 2x times ? = -4x x times ? = -5x What factors does 2x 2 & - 5x have in common? x Page 34

5. FACTOR ____________________________ Last term 1 st Term Factor b acac __________________ = __________________ 3x 2 + 7x + 1 3(1) = 3 7 Since the product is positive, the factors must have same signs as b What are factors of 3 that will give you 7? Factors prime Create your x-box Page 34 None, therefore it is prime HW #15: Red text p. 218 #s 1 – 7, and p. 222 #s 1-15 (1 st column)

FACTOR ____________________________ Last term 1 st Term Factor b acac __________________ = __________________ Factors

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