Factoring Quadratics

Learning Intention/Success Criteria LI: We are learning to factor quadratics SC: I know how to -recognize if a quadratic can be factored -identify the roots and y-intercept of a quadratic -identify the solutions of the equation by factoring -multiply and add integers -check my work by multiplying binomials -factor out the GCF

Steps for factoring quadratics 1. Pull out the GCF or if first term is negative, factor out the negative 2. Find A * C 3. Factor AC to add to B 4. Split bx 5. Fill out box 6. Check work

Example 1: Factor x2 + 5x + 6 1. Pull out the GCF x2 + 5x + 6 2. Find A * C A: B: C: 1 5 6 A * C: 1 * 6 = 6 3. Factor AC to add to B A * C: 6 1 6 = 7 2 3 = 5

4. Split bx x2 + 5x + 6 x2 + 2x + 3x + 6 5. Fill box x + 2 x x2 + 2x + 3 + 3x 6 (x + 2)(x + 3)

6. Check your work (x + 2)(x + 3) **If A, B, and C are all positive, then both factors will be positive x * x = x2 x * 3 = 3x 2 * x = 2x 2 * 3 = 6 x2 + 3x + 2x + 6 x2 + 5x + 6

Example 2: Factor x2 + 2x – 8 1. Pull out the GCF x2 + 2x – 8 2. Find A * C A: B: C: 1 2 -8 A * C: 1 * -8 = -8 3. Factor AC to add to B A * C: -8 -1 8 = 7 -2 4 = 2

4. Split bx x2 + 2x – 8 x2 – 2x + 4x – 8 5. Fill box x - 2 x x2 - 2x + 4 + 4x - 8 (x + 4)(x – 2)

6. Check your work (x + 4)(x – 2) **If B and C are opposite signs, then only one factor will be positive x * x = x2 x * 4 = 4x -2 * x = -2x -2 * 4 = -8 x2 + 4x – 2x – 8 x2 + 2x – 8

Example 3: Factor x2 – 13x + 42 1. Pull out the GCF x2 – 13x + 42 2. Find A * C A: B: C: 1 -13 42 A * C: 1 * 42 = 42 3. Factor AC to add to B A * C: 42 -1 -42 = -43 -2 -21 = -23 -3 -14 = -17 -6 -7 = -13

4. Split bx x2 – 13x + 42 x2 – 6x – 7x +42 5. Fill box x - 6 x x2 - 6x - 7 - 7x + 42 (x – 7)(x – 6)

6. Check your work (x – 7)(x – 6) **If B is negative and C is positive, then both factors will be negative x * x = x2 x * -7 = -7x -6 * x = -6x -7 * -6 = 42 x2 – 7x – 6x + 42 x2 – 13x + 42

Example 4: Factor 5x2 + 11x + 6 1. Pull out the GCF 5x2 + 11x + 6 2. Find A * C A: B: C: 5 11 6 A * C: 5 * 6 = 30 3. Factor AC to add to B A * C: 30 1 30 = 31 2 15 = 17 = 13 3 10 5 6 = 11

4. Split bx 5x2 + 11x + 6 5x2 + 5x + 6x + 6 5. Fill box x + 1 5x 5x2 + 5x + 6 + 6x 6 (5x + 6)(x + 1)

6. Check your work (5x + 6)(x + 1) **If A, B, and C are all positive, then both factors will be positive 5x * x = 5x2 5x * 1 = 5x 6 * x = 6x 6 * 1 = 6 5x2 + 5x + 6x + 6 5x2 + 11x + 6

Example 5: Factor -2x2 – 9x + 7 1. Pull out the GCF -2x2 + 9x – 7 -1(2x2 – 9x + 7) 2. Find A * C A: B: C: 2 9 -7 A * C: 2 * -7 = -14 3. Factor AC to add to B A * C: -14 -1 -14 = -13 -2 -7 = -9

4. Split bx -1(2x2 – 9x + 7) -1(2x2 – 2x – 7x + 7) 5. Fill box x - 1 2x 2x2 - 2x - 7 - 7x + 7 (2x – 7)(x – 1)

6. Check your work (2x – 7)(x – 1) **If B is negative and C is positive, then one factor will be positive 2x * x = 2x2 2x * -1 = -2x -7 * x = -7x -7 * -1 = 7 -1(2x2 – 2x – 7x + 7) -1(2x2 – 9x + 7) -2x2 + 9x - 7