1. Algebra 2 cc Section 2.2 Solve quadratic equations by factoring
Note: 3∙2 = 6, so 2 and 3 are factors of 6
Factoring is the inverse of multiplying . There are several factoring techniques.
Factor out the greatest common factor (GCF)
2x2+ 6x x3+ 12x2
22x3 - 11x2 + 33x y - 7

2. Difference of Squares Factoring Pattern a2- b2 = (a+b)(a-b) (conjugates)
Factor x2 – 9 4x – 16y2
5x u2 + 8u

3. ax2 + bx + c is a quadratic trinomial
Note: (x+2)(x+3) = x2 + 5x + 6, so (x+2) and (x+3) are factors of x2 + 5x + 6
Its factors are in the form (rx+p)(sx+q) where r∙s = a and p∙q = c, and rq+ps = b
ax2 + bx + c is a quadratic trinomial
Factor
x2 + 4x + 3
(x+3)(x+1)
x2 - 7x + 10
(x-2)(x-5)

4. Factor
x2 - x – 6 (x-3)(x+2) x2 + 2x – 8 (x+4)(x-2)

5. Factor
2x2 + 4x + 2 2(x2 + 2x + 1) 2(x+1)(x+1) 3x2 - 17x + 10 (3x – 2)(x – 5) 12x2 - 25x – 7 (4x + 1)(3x – 7)

6. A Quadratic Equation takes the form: ax2 + bx + c = 0 It has two solutions.
Solve x2 - 3x - 4 = 0
To solve a quadratic equation by factoring:
Set in standard form
ax2 + bx + c = 0
Factor the quadratic
Set each factor equal to zero
Solve each resulting equation
Check solution

7. Solve
k2 + 24k = 0
2y2 – 4y - 8 = -y2 + y

8. solve
-3b = -3b

10. assignment
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Problems all