Trinomials+Where+a+Does+Not+Equal+1

Trinomial Where A ≠ 1

There are two methods to factoring trinomials where "a" doesn't equal one.

__Method One__ is reverse FOIL-Guess and check (Use this when "a" is a prime number) Factor: 3x 2 -14x-24 3 is prime, so the first terms in the binomials have to be 3x and x. "c" is negative, so the signs in the binomials have to be different. Find two numbers whose product is -24, then guess and check them using FOIL Your options are: 6,-4 -6,4  8,-3  -3,8  -2,12  2,-12  Take your first option and put it in your binomials (3x-4)(x+6)=3x 2 +14x-24 That didn't work, so try switching the numbers (3x+6)(x-4)=3x 2 -6x-24 That didn't work either, so move onto the next set of numbers (3x-6)(x+4)=3x 2 +6x-24 Switch the numbers (3x+4)(x-6)=3x 2 -14x-24 Success!

(If you do not find the right set of numbers, don't get discouraged. This is why this method is called "guess and check". Just keep trying until you find the pair that works.)

__Method Two__ is to factor by grouping (Use this when "a" is a composite number) Factor: 4x 2 -4x-3 4 is composite, so factor by grouping. Multiply a and c (4 and -3) together 4*-3=-12. Find two factors of -12 whose sum is -4. 1+-12=-11 -1+12=11  -3+4=1  3+-4=-1  -2+6=4  2+-6=-4  Divide the middle term (4x) into 2x and -6x. 4x 2 +2x-6x-3 Split the first two terms from the last two, and make them into binomials with a plus sign in the middle. (4x 2 +2x)+(-6x-3) Now find the GCF of each binomial. 2x(2x+1)-3(2x+1) If the two binomials are they same, you did it right. Take the GCFs (2x,-3) and put them in one binomial. (2x-3) Use the binomial left when you factor out the GCF as the other factor. (2x+1)(2x-3) FOIL just to make sure you got it right. (2x+1)(2x-3)=4x 2 -4x-3