71 FACTORS AND GREATEST COMMON FACTORS

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7-1 FACTORS AND GREATEST COMMON FACTORS

• Define
• Factor 3. Prime Number
• GCF 4. Composite
• Find prime factorization
• make a tree
• 40 300

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• C. Find GCF
• List of factors method
• List all factors
• Find the largest same factor
• Tree method
• Make a tree
• Find the same factors
• Multiply factors

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7-2 FACTORING USING THE DISTRIBUTIVE PROPERTY

• Review simplifying
• 3(x5) 3. 2c(5c 8)
• y(5y 6) 4. 4xy(6x 5y3)
• Factoring using GCF
• Find GCF
• GCF

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• C. Examples

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7-3 FACTORING BY GROUPING

• Review GCF factoring
• 4x 20
• 12ab 8a
• 25c5a-15b
• 12x17

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• B. Steps
• Group in pair using ( )
• Factor each ( ) with GCF
• factor out (same)
• Check by simplifying

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• C. Examples

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7-5 FACTORING TRINOMIALS

• Review simplifying
• (x2)(x3) 2. (2y-5)(y3)
• Factoring x2 bx c
• Make a chart
• (x f1) (x f2)
• Check

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• C. Factoring ax2 bx c
• Multiply (a)(c)
• Make a chart
• Rewrite replace b with (f1 f2)
• Distribute x
• Factor by grouping
• Check

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• D. Examples
• x2 5x 6
• 2x2 x 15

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7-6 FACTORING DIFFERENCE OF SQUARES

• Review simplifying
• (x3)(x-3) 2. (2x5)(2x-5)
• Requirements
• Must be a binomial
• Must be subtraction
• Both parts perfect squares

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• C. Steps
• Does it meet the requirements
• D. Examples
• x2 9 3. c2 25
• 4x2 49 4. 2y2 50

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7-7 PERFECT SQUARES AND FACTORING

• Review simplifying
• (x4)(x4)
• (y3)(y3)
• (h-5)2

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• B. Requirements
• Trinomial
• First and last part perfect squares
• Middle
• C. Steps
• a2 2ab b2 (a b)2
• a2 - 2ab b2 (a - b)2

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• D. Examples
• x2 8x 16
• y2 6y 9
• h2 10h 25

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7-8 SUMMARY OF FACTORING

• Factoring Methods
• GCF
• Difference of squares
• Grouping
• Perfect square trinomials
• Reverse foil
• New Improved reverse foil

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7-9 SOLVING EQUATIONS BY FACTORING

• Review solving
• x 9 5
• 5x 3 2x 6
• x2 4x x2 8
• Zero product property
• If ab0, then a0 or b0

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• C. Steps
• Set equation 0
• Move parts using or
• 2. Factor
• 3. Set all parts 0
• 4. Solve all parts
• 5. answer

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• D. Examples
• x2 9
• x(x 8) 0
• x2 -5x 6
• 4x2 -8x