# Thread: Is there a better way to factor this trinomial?

1. ## Is there a better way to factor this trinomial?

My time is pretty limited when I take tests and quizzes, and this problem seems like it would take too long for what its worth given my current knowledge.

36y^2-35+12y

i can get 36y^2+42y-30y-35 and do the rest from there. However I am wondering if theres a quicker way to figure this problem out. The way I get this is:

36*-35=-1260
42*-30 = -1260
42+-30= 12

I dont know how im supposed to just know that or calculate that in a reasonable amount of time. so im wondering is there some trick to factoring trinomials like this in a faster, more efficient way? I typically use the grouping method. Hopefully my only options arent limited to pure trial and error.

2. Originally Posted by NecroWinter
My time is pretty limited when I take tests and quizzes, and this problem seems like it would take too long for what its worth given my current knowledge.

36y^2-35+12y

i can get 36y^2+42y-30y-35 and do the rest from there. However I am wondering if theres a quicker way to figure this problem out. The way I get this is:

36*-35=-1260
42*-30 = -1260
42+-30= 12

I dont know how im supposed to just know that or calculate that in a reasonable amount of time. so im wondering is there some trick to factoring trinomials like this in a faster, more efficient way? I typically use the grouping method. Hopefully my only options arent limited to pure trial and error.
You could try simplifying as follows...

$\displaystyle 36y^2+12y-35=(6y)^2+2(6y)+7(-5)=(6y+7)(6y-5)$

3. Originally Posted by Archie Meade
You could try simplifying as follows...

$\displaystyle 36y^2+12y-35=(6y)^2+2(6y)+7(-5)=(6y+7)(6y-5)$
Why dont they just show it that way initially? Jeez. Thats so much simpler. Thank you.

4. True.
We don't see the word "substitution" mentioned often when factoring these...

$\displaystyle x=6y$

$\displaystyle 36y^2+12y-35=(6y)(6y)+2(6y)-35=x^2+2x-35$

Now we need the factors of -35 to combine and give us 2 (the coefficient of x).

$\displaystyle (x+a)(x+b)=x^2+2x-35\Rightarrow\ a+b=2,\;\;ab=-35$

The numbers are $\displaystyle 7,\;\;-5$