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2015-11-22
FACTORING REVIEW
Greatest Common Factor
6x2 + 8
The factors are:
2x (3x + 4)
> Find the common factor, write it outside the parenthesis and divide each term of the original
expression by the factor to determine what goes inside the parenthesis.
Reversing the Distributive Property or FOIL
For x2 + 8x + 15
> What 2 numbers multiply to get 15 and add to get 8?
(x + 3) (x + 5)
---------------------------------------For x2 + 3x - 10
> What 2 numbers multiply to get -10 and add to get +3?
(x - 2) (x + 5)
When the Coefficient of X2 is Greater Than One
3x2 - x - 4
Find the factors of
(1) Multiply the first coefficient by the last term
and replace the last term with the product.
(4) Restore the first coefficient to each variable
term:
( x - 4 ) ( x + 3 ) --> ( 3x - 4 ) ( 3x + 3 )
3x2 - x - 4
(5) Where possible, factor by "Greatest
Common Factor"
becomes 3x2 - x - 12
( 3x - 4 ) ( 3x + 3 ) --> ( 3x - 4 ) 3 ( x + 1 )
(2) Temporarily remove the first coefficient
(6) Divide by the original first coefficient
3x2
- x - 12 --->
x2
- x - 12
(3) Factor this expression using the "two
questions" method
( 3x - 4 ) 3 ( x + 1 )
__________________ = ( 3x - 4 ) ( x + 1 )
3
x2
- x - 12 = ( x - 4 ) ( x + 3 )
Solving for x by zeros
x2 + 6x - 7 = 0
(1) Factor by the "two questions" method -- what numbers multiply to get -7 and add to get 6?
( x + 7 ) ( x - 1) = 0
(2) Set each factor = 0 and solve for x
x+7=0
-7 -7
_______
x = -7
x-1=0
+1 +1
_______
x= 1
Completing the Square
Solving for x in quadratic equations ax2 + bx + c = 0
(if a is not 1 you must first divide by a)
x2 + 6x - 7 = 0
( x + 3 ) ( x + 3) = 16
(1) Move the constant term to the right side
(4) Re-write the left side as a binomial squared
x2
+ 6x - 7 = 0
+7 +7
____________
( x + 3 )2 = 16
(5) Take the square root of both sides:
x2 + 6x
= 7
(x  3)
2
=
(2) Divide the coefficient of X by 2 and square
it. Add the result to both sides.
x + 3 = 4
x2 + 6x + (6/2)2
(6) Solve for x
= 7 + (6/2)2
x2 + 6x + 9 = 7 + 9
x2 + 6x + 9 = 16
(3) You have created a perfect square on the
left side. Factor it
16
x + 3 = 4
-3
-3
_________
x
= -3 4 Answer x = 1 x = - 7