Download Algebra 2 Section 5.2 Solve quadratic equations by factoring

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
6x3+ 12x2
22x3 - 11x2 + 33x
21y - 7
Difference of Squares Factoring Pattern
a2- b2 = (a+b)(a-b) (conjugates)
Factor
x2 – 9
5x2 - 20
4x2 - 25
2u2 + 8u
81 – 16y2
Note: (x+2)(x+3) = x2 + 5x + 6, so (x+2) and (x+3) are factors of
x2 + 5x + 6
ax2 + bx + c is a quadratic trinomial
Its factors are in the form (rx+p)(sx+q) where r∙s = a and p∙q = c,
and rq+ps = b
http://www.youtube.com/watch?v=AMEau9OE6Bs&feature=player_detailpage
Factor
x2 + 4x + 3
(x+3)(x+1)
x2 - 7x + 10
(x-2)(x-5)
Factor
x2 - x – 6
(x-3)(x+2)
x2 + 2x – 8
(x+4)(x-2)
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)
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:
1. Set in standard form
ax2 + bx + c = 0
2. Factor the quadratic
3. Set each factor equal to
zero
4. Solve each resulting
equation
5. Check solution
Solve
k2 + 24k + 144 = 0
2y2 – 4y - 8 = -y2 + y
solve
-3b2 + 90 = -3b
assignment
• Page 260
• Problems 65-78 all