Trinomial+Where+A+=1

Factoring quadratic trinomials when a=1 is one of the easiest things to do in algebra! **

A quadratic formula looks like ax^2 (^2 signifies squared) + bx + c, and when a = 1, it makes life a lot easier.

Let's walk this through.


 * 1) x^2 + x - 6 This is where we start, with a trinomial quadratic. Now let's start to unFOIL.
 * 2) (x )(x ) This is what makes factoring trinomials when a=1 easy. With "a" being 1, we know that the leading terms will just be x.
 * 3) Once we know that the first terms will be "x" we know that the second numbers have to multiply and equal "c" from the original equation and also add together to equal "b" from the original equation.
 * 4) Next we need to find combinations of numbers that, when multiplied, equal -6. The possible combinations are: -6 and +1, +6 and -1, +3 and -2, and +2 and -3.
 * 5) Now we need to find combinations of numbers that, when added together, equal term "b", which in this case is 1, and also multiply together to equal term "c", which in this case is -6.
 * 6) We already made a list of possible combinations with a product of -6, so lets test them to see if they add together to equal 1. -6 + 1 = -5, nope. 6 + -1 = 5, nope. -3 + 2= -1, nope. 3 + -2 = 1, AWWWWWW YEAAHHHHHHH!
 * 7) So our answer comes out to be x^2 + x - 6=(x+3)(x-2).

Let's do an example now.


 * 1) x^2 - 15x - 16
 * 2) (x )(x )
 * 3) possible combinations where product equals -16: -16 and 1, 16 and -1, 4 and -4, 8 and -2, -8 and 2
 * 4) add each combination to find one that equals - 15, and you get your two terms: -16 and 1
 * 5) (x - 16)(x + 1)

<span style="display: block; font-family: 'Comic Sans MS',cursive; text-align: center;"><span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">//**SUPER SECRET SHORT CUT (Classified Information)// <span style="display: block; font-family: 'Comic Sans MS',cursive; text-align: center;"><span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">If the coefficient of x^s is 1, then x^2 + bx +c = (x + m)(x + n) <span style="display: block; font-family: 'Comic Sans MS',cursive; text-align: center;"><span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">where m and n __multiply to get c__  <span style="display: block; font-family: 'Comic Sans MS',cursive; text-align: center;"><span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">and m and n __add to get b.__

<span style="font-family: 'Comic Sans MS',cursive;">CREDIT: <span style="font-family: 'Comic Sans MS',cursive;">Regents Prep Algebra Page

<span style="font-family: 'Comic Sans MS',cursive;">ADDITIONAL LINKS: <span style="font-family: 'Comic Sans MS',cursive;">A really intense example. Best factoring game ever