Trinomial+Where+A+does+not+=+1

Factoring When a Does Not Equal Zero

You know to use these methods when the coefficient in front of the quadratic term (_x 2 ) is greater than one

** Method 1: Reverse FOIL ** - Guess and Check EXAMPLE 1: Factor 2x 2 -7x+6 EX: (2x ) (x )
 * Since the first term in 2x 2, the first terms of the two binomials have to be 2x and x.

EX: (2x- ) (x- ) EX: (2x-1) (x-6) (2x-6) (x-1) (2x-2) (x-3) (2x-3) (x-2)
 * Since the 6 is positive and the -7x is negative, the two signs of the two binomials have to be negative
 * Then, find two factors of 6 that will complete the factors. It must be 1 and 6 OR 2 and 3.
 * Finally, Try all of the above possibilities until one works out to be the quadratic you started out with

EX: (2x-3) (x-1)


 * TA DA!!!!

If the Terms in the Parenthesis have a GCF greater than 1, it will not work

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** Method 2: Factor By Grouping ** EXAMPLE: Factor 2x 2 -7x+6 EX: ac= 12
 * Multiply a and c

EX: -1+-12=-13 -2+-6 = -8 -3+-4=-7 EX: 2x 2 -3x-4x+6
 * Find two factors of 12 whose sum is -7.
 * Since the 6 is positive and the -7x is negative both factors must be negative
 * Then the factors become the middle terms

EX: (2x 2 -3x)+(-4x+6)
 * Group the first two terms and the last two terms

EX: x(2x-3)-2(2x-3)
 * Factor out the GCF from each of the group

*Factor out a -2 from the second group to get the grouped terms equil*

EX: (2x-3) (x-1)
 * Factor out the groups


 * TA DA!!!!

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