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Factoring to Solve Equations

Factoring to Solve Equations. Date: ___________. Example 1: Solve . Steps: Rearrange the question so it is in standard form (ax 2 + bx + c = 0). a) x 2 – x = 12. 2. Factor the quadratic. x 2 – x – 12 = 0. Set each bracket = 0 and solve to find the roots. (x – 4)(x + 3) = 0.

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Factoring to Solve Equations

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  1. Factoring to Solve Equations Date: ___________

  2. Example 1: Solve Steps: Rearrange the question so it is in standard form (ax2 + bx + c = 0) a) x2 – x = 12 2. Factor the quadratic. x2 – x – 12 = 0 Set each bracket = 0 and solve to find the roots. (x – 4)(x + 3) = 0 x + 3 = 0 x – 4 = 0 A  -1 M -12 -4 3 x = -3 x = 4 b) 4x2 = – 23x – 15 4x2 + 23x + 15 = 0 A  23 M 60 20 3 4x2 + 20x + 3x + 15 = 0 4x(x + 5) + 3(x + 5) = 0 (x + 5)(4x + 3) = 0 Don’t forget the =0 each time 4x + 3 = 0 x + 5 = 0 x = - ¾ x = -5

  3. You don’t use the 2 since it is the ‘a’ value. It is just the vertical stretch! c) 2(x – 1)(x + 5) = 0 x – 1 = 0 x + 5 = 0 x = -5 x = 1 d) 2x (x + 7) = 0 x = 0 x + 7 = 0 x = -7 e) 3x(x – 2) = 105 A  -2 M -35 -7 5 3x2 – 6x – 105 = 0 3(x2 – 2x – 35) = 0 3(x – 7)(x + 5) = 0 x = 7 x = -5 Your homework is Pg. 279 # (2 – 6) a,c, 7, 8, 11, 13, 14

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