05 Solving by Factoring.notebook
April 09, 2015
Name the 5 Methods of Factoring
GCF
Difference of 2 Squares
UnFOIL
Perfect Trinomial Squares (Butterfly)
Grouping
Which method of factoring should
GCF
always be tried first?
Once the GCF is removed, are you necessarily done factoring?
NO! You look at what is left in
the parenthesis and see of one
of the other methods will work to
factor further
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05 Solving by Factoring.notebook
April 09, 2015
Factor
1. x2 – 36
2. 16x2 – 36
3. x2 + 4x + 3
4. 6x3 – 21x2 – 27x
5. 25x2 – 90x + 81
6. 4x3 – 20x2 – 9x + 45
1. x – 36
2
Factor
(x - 6)(x + 6)
3. x2 + 4x + 3
(x + 3)(x + 1)
5. 25x2 – 90x + 81
(5x - 9)(5x - 9)
2. 16x2 – 36
4(2x - 3)(2x + 3)
4. 6x3 – 21x2 – 27x
3x(2x2 - 7x - 9)
3x(2x - 9)(x + 1)
6. 4x3 – 20x2 – 9x + 45
4x2 (x-5) - 9(x-5)
(4x2 -9)(x-5)
(2x-3)(2x+3)(x-5)
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05 Solving by Factoring.notebook
April 09, 2015
Solving Quadratic Equations
To solve a quadratic equation means to find the roots (points where the parabola crosses
the x-axis) of the equation.
y = x2 + 4x + 3
Direction: Up
Width: Regular
Axis: x = -2
Vertex: (-2, -1)
Roots: (-3, 0) & (-1, 0)
Solving Equations Algebraically
1. x + 4 = 0
x = -4
2. 4x = 0
x=0
3. 4x + 4 = 0
x = -1
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05 Solving by Factoring.notebook
April 09, 2015
Look at the Last Problem
Can you factor 4x + 4?
Factor: 4x + 4
4(x + 1)
What is the 4 doing to (x + 1)?
Multiplying it
If we set 4(x + 1) = 0 what does that mean?
Since 4 and (x+1) are multiplying each
other, (x+1) must equal 0 because 4≠0
Zero Product Property
For all numbers (call them) "a" and "b" if a b = 0, then
a=0
b=0
or both(a&b) = 0
What does that mean ???
For Example: (x – 2)(x – 4) = 0
1. Do we know which factor is zero? No
2. So, set them both equal to zero & solve
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05 Solving by Factoring.notebook
April 09, 2015
Solving Quadratic Equations using Factoring
Steps:
1. Set equation equal
to zero
Example:
x2 – 6x + 8 = y
2. Factor completely
3. Set each factor equal
to zero
4. Solve for each factor
5. Check by plugging
answers back in
R: (2, 0) & (4, 0)
Solve by Factoring
1. x2 ­ x ­ 20 = 0
R: (5, 0) & (-4, 0)
2. 2x2 + 3x ­ 9 = 0
R: (-3, 0) & (3/2, 0)
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05 Solving by Factoring.notebook
April 09, 2015
Solve by Factoring
4. 5x2 ­ 50 = 45x
3. x2 = 7x
R: (0, 0) & (7, 0)
R: (10, 0) & (-1, 0)
Today's Math Journal Questions
Day 4 Question: ______________________
(Date)
What is being found when you give me the roots of a
quadratic equation?
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