Transcript WHAT IS FACTORING?

WHAT IS FACTORING?
•Writing an expression as a product of it’s factors
•The reverse process of multiplying an expression
Different ways of Factoring
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Factor out a Greatest Common Factor
Factor a polynomial with 4 terms by grouping
Factoring Trinomials of the form x² +bx+c
Factoring Trinomials of the for ax² +bx+c
Prime Polynomials
Other Polynomials and source information
Factoring out the GCF
• Note: The GCF is the largest monomial that is factor of
each term of the polynomial
• Step 1: Identify the GCF
• Step 2: Divide the GCF out of every
term
Factoring out the GCF
• Example 1: 8(y)^7-4(y)^5+2(y)^4
• Step 1: Pick out GCF
– GCF= 2(y)^4
• Step 2: Divide the GCF out of every term
- 2(y)^4[4(y)^3-2y+1]
Factoring out the GCF
• Example 2: 4(x-2)+x(x-2)
• Step 1: GCF=(x-2)
• Step 2: (x-2)(4+x)
Factoring a Polynomial with 4
Terms by Grouping
• Note: If you have 4 terms with no GCF try grouping
• Step 1: Group the 1st 2 terms and then the
last 2 terms
• Step2: Factor out GCF from each
separate binomial
• Step3: Factor out common binomial
Factoring a Polynomial with 4
Terms by Grouping
• Example: x³+2x²+6x+12
• Step 1: (x³+2x²)+(6x+12)
• Step 2: x²(x+2) +6(x+2)
* Factor out x² from 1st ( )
* Factor out 6 from 2nd ( )
• Step 3: (x+2)(x²+6)
*Divide (x+2) out of both parts
Factoring Trinomials that Look Like
x²+bx+c
• Step 1: Set up ( )( )
• Step 2: Find the factors that go in 1st position
– For x² it’s always x
• Step 3: Find the factors that go in 2nd position
-Their product must = c
-Their sum must = b
-If c’s positive then the factors will have the same sign depending on b
-If c’s negative then the factors will be opposite depending on b
-Make a chart if needed
Factoring Trinomials that Look Like
x²+bx+c
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Example: a²-6a-16
Step 1: Set up ( )( )
Step 2: (a )(a )
Step 3: Product of factors must = -16
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List factors: 1,-16 ; -1,16 ; 2, -8 ; -2,8 ; -4,4 ; 4,-4
Look at your list and see which pairs adds up to -6
You should pick 2,-8
Place those in the 2nd positions
(a+2)(a-8)
Factoring Trinomials that Look Like
ax²+bx+c where a≠1
• Step 1: Set up ( )( )
• Step 2: Use trial and error
– Factors of a will go in 1st positions
– Factors of c will go in 2nd positions
Factoring Trinomials that Look Like
ax²+bx+c where a≠1
• Example: 5x²+8x+3
• Step 1: Set up ( )( )
• Step 2: Find factors of 5x²
• The only factors are 5x and x
– Place those in first positions
– Find factors of 3
• The only factors are 3 and 1
– Place those in 2nd positions
Solution: (5x+3)(x+1)
Prime Polynomials
• Like numbers not every polynomial is
factorable
• These are called Prime Polynomials
• You may not realize it’s prime until you
start trying to come up with factors
• An example would be x²+5x+12
– There are no factors of 12 that when added
give you 5
Other ways to factor
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Factoring a perfect square trinomial
Factoring a difference of two squares
Factoring a sum of two cubes
Factoring a difference of two cubes
• To learn how to do these go to:
– http://www.wtamu.edu/academic/anns/mps/math/mat
hlab/col_algebra/col_alg_tut7_factor.htm
Sources
• Peppard, Kim Peppard. "College Algebra
Tutorial on Factoring Polynomials."
College Algebra. Juen 22, 2003. West
Texas A&M University. 24 Sep 2006
<http://www.wtamu.edu/academic/anns
/mps/math/mathlab/col_algebra/col_alg
_tut7_factor.htm>.