Investigation 2D Factoring.notebook
October 03, 2013
Warm Up
1. Complete equivalent expressions in different ways
Investigation 2D Advanced Factoring _Warm Up
a) ____ + 6x + ______ = (_____ + ______)2
b) ____ + 6x + ______ = (_____ + ______)2
c) ____ + 6x + ______ = (_____ + ______)2
d) ____ + 3x + ______ = (_____ + ______)2
e) ____ + 3x + ______ = (_____ + ______)2
Classify the following expressions into two groups. Describe each group.
Classify the following expressions into three groups. Describe each group.
x2 ­ 8x + 16
x2 ­ 25
x2 + 8x +16
x2 ­ 16 x2 + 25
X2 +16
x2 + 10 x + 25
x2 + 10x ­ 25
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Investigation 2D Factoring.notebook
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2.12 Quadratics with A ≠1
Factor 6x2 +11x -10
Multiply by 6: 6(6x2 +11x -10)=
36x2 +11 * 6x -60
Think of 6x as the variable
let 6x = u
u2 +11u -60 Factor new quadratic
(u +15)(u - 4)
Replace u with 6x
(6x +15) (6x -4)
3(2x + 5)*2(3x -2)
=6(2x + 5)(3x - 2)
Don't forget we change the original by 6
Divide by 6
= (2x + 5)(3x - 2)
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Investigation 2D Factoring.notebook
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p167 1a­h
HW p167 #3­5
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HW p167 3 a,c,e,f, h
4, 5
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2.13 Factoring Cubics
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Investigation 2D Factoring.notebook
October 03, 2013
And if that doesn't work Look at other grouping combinations
Group the first two terms and the last two terms
Factor out a common factor in each group
If each group has a similar factor, you pull it out
Check to see if you can go any further.
27x3 +27x2 + 9x +1
Grouping the first two terms and the last two term does not give you a common factor.
Lets group the first and last term and then 2nd and 3rd.
(27x3 +1 )+ (27x2 +9x)
(3x +1)(9x2 ­ 3x +1) + 9x(3x +1)
Common factor is 3x + 1
(3x +1)(9x2 ­3x + 1 +9x)
(3x +1) (9x2 + 6x + 1) (Check if you factor what is left)
(3x + 1)(3x + 1)2 =(3x +1)3
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What can we do when grouping
doesn't help?
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Investigation 2D Factoring.notebook
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group 1
Do 1­2 p174
(X ­ 1)3 ­ 125
x3 ­ 64
27x3 + 64
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x2 ­ (3x+1)2
x3 + ax2 ­ a2x ­ a3
x3 ­ 4x2 ­ 31x + 70
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Investigation 2D Factoring.notebook
group 2
27x3 ­ 64
x2 ­ y2 + 2yz ­ z2
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x3 + 3x2 ­9x ­27
x3 ­ 4x2y ­ 31xy2 + 70y3
(x + 1)3 ­ 3x(x + 1)
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HW p175 # 4­8
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Investigation 2D Factoring.notebook
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