Algebra 1 Section 10.5 Factor quadratic trinomials and solve quadratic equations A quadratic trinomial takes the form: ax 2 + bx + c Example: (x+3)(x+4) = x 2 + 7x + 12 x·x (3+4)x 3·4 Example: factor x 2 + 3x + 2 Example: factor x 2 – 5x + 6 Example: factor x 2 – 2x -8 ax 2 + bx + c = (rx + p)(sx+q) Rule 1: r·s = a p·q = c rq + ps = b Rule 2: If c is positive, then p and q have the same sign as b. Rule 3: If c is negative, then p and q have opposite signs.

More examples Factor the following x 2 + 7x – 18 x 2 + 3x – 10 x x + 30 x 2 + 7x + 12

Student practice problems Factor the following x 2 + 9x + 20 x 2 – 8x + 12 x 2 - 1x – 30 x 2 + 2x - 15

A quadratic trinomial can not be factored if the discriminant is not a perfect square The discriminant of ax 2 + bx + c is b 2 – 4ac Example: Can x 2 + 7x + 3 be factored? b 2 – 4ac = (7) 2 – 4(1)(3) = is not a perfect square… x 2 + 7x + 3 can not be factored

Solving quadratics equations by factoring To solve a quadratic equation by factoring: 1. Set it equal to zero ax 2 + bx + c = 0 2. Factor the quadratic trinomial 3. Set each factor equal to zero 4. Solve for each factor Example: Solve x 2 + 6x = 7 1. x 2 + 6x - 7 = 0

Student problems Solve by factoring x 2 + 5x + 6 = 0 x 2 - 4x - 5 = 0 X 2 - 7x = -10

Assignment Page 607 Problems 16 – 40 even