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Factoring Statigies

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by

Ann Books

on 2 April 2014

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Transcript of Factoring Statigies

Factoring Strategies
Greatest Common Factor
Distribution Property
ab + ac = a (b + c)
ab - ac = a (b - c)
Three Terms
Standard form: ax + bx + c
Two Terms
Difference of Squares
a – b = ( a + b)(a - b)
Sum of Squares
a + b = Prime
Sum and Difference of Cubes
a + b = ( a + b )( a - ab + b )

a - b = ( a - b )( a + ab + b )
For the signs of the factors

Same Opposite Always Positive
Four Terms
Factor by Grouping
1) Factor GCF of all terms.
2) Factor GCF of pairs of terms.
(the negative GCF used when - in middle)
3) Factor Common Binomial Factors.
Berry Method
x +bx + c
(x + p)(x + q)
a = 1
AC Method
"Solve the Riddle
Split the middle"
Solve the Riddle
Write the Factors
Take out the GCF's
Solve the riddle:
Factors of c
Sum is b
Answer: p and q
Example
24x y + 30x y

(6x y )(4x ) + (6x y )(5y)

6x y (4x + 5y)
4 5 2 6
2
2
2 2
2 2
Count the number of terms
3 3 2 2
3 3 2 2
Just remember SOAP
What are Factors?
Multiply Factors to get a Product
One, Two,
Three,
Four Terms
Ha Ha Ha
2 5 2 2 5
2 5 2
GCF : 6x y
2 5
Rewrite each term using the GCF
Use the Distributive Property to factor out the GCF
1) Multiply ac.
2) Find 2 integers whose product is ac and the sum is b:
3) Rewrite the middle term: {pq = ac and p+q=b}
4) Factor by Grouping. {bx = px + qx}
ax + bx + c
2
Find Two numbers that are: Factors of AC and Sum is B
FACTOR
Write the factors
Sign Chart:

If C > 0 then the factors are the same sign
they will both be the sign of B.
If C < 0 then the factors are different signs
the larger factor is the same sign as B
Example
AC = -12 factors different signs
B = -1 larger factor (-)
Solve the Riddle: -4 and +3
2x - x + 6

(2x - 4)(2x - 3)

(x - 2)(2x - 3)
2
Write the two factors using ax with p and q:
Factor out the GCF 2 from first factor and discard
What is left is the answer
Examples
x + 7x + 12
(x + 3)(x + 4)


x - 8x + 12
(x - 6)(x - 2)


x + 7x - 18
(x + 9)(x - 2)


x - 6x - 16
(x - 8)(x + 2)
2
2
2
2
C = +12 factors same sign
B = +7 factors both (+)
Solve the Riddle: +4 and +3
C = +12 factors same sign
B = -8 factors both (-)
Solve the Riddle: -6 and -2
C = -18 factors different signs
B = +7 larger factors (+)
Solve the Riddle: +9 and -2
C = -16 factors different signs
B = -6 larger factors (-)
Solve the Riddle: -8 and +2
Examples
2x + 7x + 6
2x + 4x + 3x + 6
2x(x + 2) + 3(x + 2)
(2x + 3)(x + 2)

3x + 7x - 6
3x + 9x - 2x - 6
3x(x + 3) - 2(x +3)
(3x - 2)(x + 3)


2x - 5x + 3
2x - 3x - 2x + 3
x (2x - 3) -1 (2x - 3)
(2x - 3)(x - 1)
AC = +12 factors same sign
B = +7 both factors (+)
Solve the Riddle: +4 and +3
AC = -18 factors different signs
B = +7 larger factors (+)
Solve the Riddle: +9 and -2
AC = +6 factors same signs
B = -5 both factors (-)
Solve the Riddle: -3 and -2
Example
25x - 9
(5x) - (3) 49y + 16
(5x + 3)(5x - 3) PRIME
2
2
2
Difference of Squares
Sum of Squares
2
Step #1 Factor out the GCF
2
2
2
2
2
2
Finding the GCF
GCF is the product of the common factors
Always Choose the smallest exponent
24x y ; 30x y
4 5 2 6
24x y = 2 3 x y
30x y = 2 3 5 x y
4 5 3 4 5
*
2 6 2 6
* *
Factor each completly
GCF is 6x y
2 5
Factor Negative
Leading coefficient is Negative
-12x + 18 -2x + 8x - 14x
(-6)(2x) + (-6)(-3) -2x(x ) + -2x(-4x) + -2x(7)
-6(2x - 3) -2x(x - 4x + 7)
2
3
2
2
When your GCF is negative
the remaining factor is an opposite:
all the signs change
Step #2
Factor a Negative GCF
-ab + ac = -a (b - c)
Step #1
Example
3xy - 6x + 5y - 10
3x(y -2) + 5(y - 2)
(y - 2)(3x + 5)
8x - 20xy - 6xy + 15y
4x(2x - 5y) - 3y(2x - 5y)
(2x - 5y)(4x - 3y)
Conclusion
Steps to Success

Difference of Squares
3. Factor using AC Method
Grouping
1. Factor out the GCF
2. Count the Number of Terms
Step #3 Choose a method based on the number of terms you have
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