FactoringPart1.notebook
February 24, 2011
Geometry
Ch.Factoring Notes Page 27
P27 Factoring (Part 1)
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FactoringPart1.notebook
February 24, 2011
Double Distributing
Standard Form: Highest Exponent First, Second Highest Next, Etc...
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FactoringPart1.notebook
February 24, 2011
Factoring ­ (Opposite of Distributing)
Rewriting an expression as the product of its factors.
Numbers are factors if the first divides evenly into the second. Greatest Common Factors (GCF)
Greatest factor that divides evenly
into each term of an expression.
2
4x + 20x ­12
2
9n ­ 24n
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FactoringPart1.notebook
February 24, 2011
Basic Factoring a = 1
ax2 + bx + c
Find two numbers that Add to b and Multiply to ac
1x2 + 6x + 8
1x2 ­ 7x + 12
2 and 4
­3 and ­4
Fraction Method
Factoring ­ (Opposite of Distributing)
ax2 + bx + c
Find two numbers that Add to b and Multiply to ac
2x2 ­ 11x + 15
ac and b
­1 x ­30
­2 x ­15
­3 x ­10
­5 x ­6
Write 2 fractions
Leading Coefficient/Each Number
2/­5 and 2/­6 (Reduce the Fractions)
2/­5 and 1/­3 (Keep the Neg in the bottom)
(2x ­ 5)(1x ­ 3)
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FactoringPart1.notebook
February 24, 2011
Fraction Method
Factoring ­ (Opposite of Distributing)
ax2 + bx + c
Find two numbers that Add to b and Multiply to ac
2x2 + x ­ 28
ac and b
­1 x 56
­2 x 28
­4 x 14
­7 x 8
Write 2 fractions
Leading Coefficient/Each Number
2/­7 and 2/8 (Reduce the Fractions)
2/­7 and 1/4 (Keep the Neg in the bottom)
(2x ­ 7)(1x + 4)
Factoring ­ Examples
6x2 + 23x + 7
2x2 + 5x + 2
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FactoringPart1.notebook
February 24, 2011
Extra
Factoring ­ Examples
7x2 ­ 26x ­ 8
5x2 ­ 14x ­ 3
Factoring ­ GCF First (Always)
20x2 + 80x + 35
2x2 + 12x + 10
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FactoringPart1.notebook
February 24, 2011
Special Patterns
Difference of Squares
a2 ­ b2 = (a + b)(a ­ b)
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2
49x ­ 9
9x ­ 16
Difference of Squares: Examples
(c + 4)(c ­ 4)
(5m + 11)(5m ­ 11)
(8m + 9)(8m ­ 9)
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FactoringPart1.notebook
February 24, 2011
HW #30
Factoring WS#1 (First Column) Front and Back
Please put your name and class period at the top of
the homework. Also include the homework number.
Terms:
Distributing
Double Distributing
Factoring
GCF
Factor using Fractions
Difference of Squares
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