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4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
4.2
Solving Quadratic Equationsby Factoring
The methods of factoring from grade 10 math:
1. Greatest common factor
5x2 + 20x 9x2 27x
2x36x28x
4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
2. Short trinomials
x2 + 11x + 30 x2 + 5x 14
x2 9x + 20
3. Long trinomials (decomposition / box method)
2x2 + 11x + 12 6x2 + 13x 5
10x2 22x + 4
4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
4. Difference of Squares
x2 16 25x2 36 100x2 81
Factoring FlowchartGCF
2 Terms 3 Terms
Diff. of Squares Short Tri. Long Tri.
Decomposition
or Box Method
4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
Some expressions will not factor (DNF)
examples:
4x2 + 25 x2 + 7x + 16
Super Fun Time: Factoring Review Worksheet
++
We are able to use our factoring skills to solve some quadratic equations:
Example 1: Solve the following for x:
x2 + 6x + 8 = 0
To do this we use The zero product property:
if A x B = 0, then either A = 0, B = 0 or both = 0
4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
Example 2: Solve the following by factoring
4x2 + 12x 16 = 0
4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
25
Example 3: Solve the following by factoring:
4.2 Factoring Quadratic Equations (Solutions).notebook September 29, 2015
Doing these is a Factor in your Learning:
p. 230
3(ac, solve if = 0), 5a, 7acde, 8acd, 9ade, 10(ac), 30(ac)
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