# 9-6 X-box Factoring ax 2 +bx+c. X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how.

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9-6 X-box Factoring ax 2 +bx+c

X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how to factor quadratic equations with a number in front of the x 2 using the x-box method!

Factor the x-box way middle left*right m n y = ax 2 + bx + c Right Term Left Term n m GCF

Factor the x-box way Example: Factor 3x 2 -13x -10 -13 (3)(-10)= -30 -15 2 -10 -15x 2x 3x 2 x-5 3x +2 3x 2 -13x -10 = (x-5)(3x+2)

Examples continued Factor 2x 2 - 5x - 7 a) b) -14 -5 2x 2 -7x 2x -7 x 2x-7 +1 Solution: 2x 2 - 5x – 7 = (2x - 7)(x + 1 ) -7 2

Examples continued Factor 15x 2 + 7x - 2 a) b) -30 7 15x 2 10x -3x -2 5x 3x+2 Solution: 15x 2 + 7x – 2 = (3x + 2)(5x - 1 ) 10 -3

Examples continued Factor 3x 2 - 17x + 10 a) b) 30 -17 3x 2 -15x -2x 10 3x x-5 -2 Solution: 15x 2 + 7x – 2 = (3x -2)(x - 5 ) -15 -2

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