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 September 24th, 2017, 02:38 PM #1 Newbie   Joined: Sep 2017 From: Canada Posts: 1 Thanks: 0 Factoring! When factoring the RIGHT side of a trinomial if there are multiple correct answers then how is it decided which one is correct? For example y^2-4y-12 The answer could either be (y-6)(y+2) (y+6)(y-2) (y-4)(y+3) (y+4)(y-3) (y-1)(y+12) (y+1)(y-12) I would assume the correct answer would be (y+4)(y-3) but that actually factors the whole not just the right. The book states the correct answer as (y+2)(y-6) But how is that decided?
 September 25th, 2017, 03:37 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,781 Thanks: 1432 There is only one correct factorization ... $y^2-4y-12=(y-6)(y+2)$ ... all the rest will not yield the linear term $-4y$ when expanded (multiplied).
September 25th, 2017, 02:04 PM   #3
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Quote:
 Originally Posted by Kejntesh When factoring the RIGHT side of a trinomial if there are multiple correct answers then how is it decided which one is correct? For example y^2-4y-12 The answer could either be (y-6)(y+2) (y+6)(y-2) (y-4)(y+3) (y+4)(y-3) (y-1)(y+12) (y+1)(y-12) I would assume the correct answer would be (y+4)(y-3) but that actually factors the whole not just the right.
Here's a tip- do not "assume" in mathematics. It is okay to "guess" if you then check. If you were to "guess" that (y+ 4)(y- 3) is a factorization of y^2- 4y- 12, you can check by doing the multiplication: (y+ 4)(y- 3)= y(y- 3)+ 4(y- 3)= y^2- 3y+ 4y- 12= y^2+ y- 12, NOT y^2- 4y- 12 so that is NOT correct.

Quote:
 The book states the correct answer as (y+2)(y-6) But how is that decided?
(y+ 2)(y- 6)= y(y- 6)+ 2(y- 6)= y^2- 6y+ 2y- 12= y^2- 4y- 12.

In general, in order to factor y^2+ ay+ b into (y+ u)(y+ v) you need to find two numbers, u and v, such that uv= b and u+ v= a. Here, a= -4 and b= -12. How can you factor -12? One way is (-1)(12) but -1+ 12= 11, not -4. Another is, of course, (-12)(1) but -12+ 1= -11, not 4. Another is 3(-4) but 3- 4= -1 not -4. (-3)(4) is 12 but -3+ 4= 1, not -4. (-2)(6)= -12 but -2+ 6= 4 not -4. (2)(-6)= -12 and 2- 6= -4! AHA!

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