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Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. X- Box. Product a∙c. factors. factors. Sum b. 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

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Solving Quadratic Equations by Factoring

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  1. Solving Quadratic Equations by Factoring

  2. X- Box Producta∙c factors factors Sumb

  3. 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: • Basic x-solve problems • General form of a quadratic equation

  4. Solve the x-box way Example: Solve 3x2 -13x -10 = 0 by factoring. x -5 (3)(-10)= -30 3x -15x 3x2 2 -15 +2 -13 2x -10 3x2 -13x -10 = 0 (x-5)(3x+2) = 0 X = 5, -2/3

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

  6. -12 4 Examples Solve using the x-box method. 1. x2 + 4x – 12 = 0 x +6 x 6x 6 -2 -2 -2x -12 Solution: x2 + 4x – 12 = 0 (x + 6)(x - 2) = 0 x = -6,2

  7. Examples 2. x2 - 9x + 20 = 0 x -4 -4-5 20 -9 x x² -4x -5 -5x 20 Solution: x2 - 9x + 20 = 0 (x - 4)(x - 5) = 0 x = 4, 5

  8. Examples 3. 2x2 - 5x – 7 = 0 2x -7 -72 -14 -5 x -7x 2x² +1 2x -7 Solution: 2x2 - 5x – 7 = 0 (2x - 7)(x + 1) = 0x = 7/2, -1

  9. Examples 4. 15x2 + 7x – 2 = 0 3x +2 -30 7 5x 10x 15x² 10-3 -1 -3x -2 Solution: 15x2 + 7x – 2 = 0 (3x + 2)(5x - 1) = 0x = -2/3, 1/5

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