X-box Factoring.

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Presentation transcript:

X-box Factoring

X-box Factoring This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how to factor quadratic equations using the x-box method Background knowledge needed: General form of a quadratic equation Dividing a polynomial by a monomial using the box method

Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)= -30 x -5 -15 2 -13 2x -10 +2 3x2 -13x -10 = (x-5)(3x+2)

First and Last Coefficients Factor the x-box way y = ax2 + bx + c Base 1 Base 2 Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum Height

Examples Factor using the x-box method. 1. 6x2 + 7x +2 3x 2 6x2 4x 2x 12 7 6x2 4x 3x -2 2x 3 4 1 Solution: 6x2 + 7x –2 = (x + 2)(x +1)

Examples continued 2. x2 - 9x + 20 x -4 x x2 -4x -5x 20 a) b) x -4 -4 -5 20 -9 x x2 -4x -5x 20 -5 Solution: x2 - 9x + 20 = (x - 4)(x - 5)

Examples continued 3. 2x2 - 5x - 7 2x -7 x 2x2 -7x 2x -7 a) b) 2x -7 -14 -5 -7 2 x 2x2 -7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

Examples continued 3. 15x2 + 7x - 2 3x +2 5x 15x2 10x -3x -2 -30 7 5x 15x2 10x -3x -2 10 -3 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

Independent Practice Do the worksheet using the x-box method. Show all your work to receive credit– don’t forget to check by multiplying!

Factor the x-box way (3)(-10)= -30 x -5 3x 3x2 -15x -15 2 -13 2x +2