Factoring the hard trinomial containing a negative

Using decomposition method to factor a hard trinomial that contains a negative sign. This video is the 11th out of 16 in the Factoring series. The other three series are "Solving Equations", "Word Problems" and "Graphing".

Category:

Howto & Style

Tags:

• mathematics
• factoring
• series

[minkusbc]

Break up 6 into 2 x 3 and divide left bracket by 2 and right bracket by three.

[valumni]

Sorry to bother you but do the terms in the parenthese have to be identical? I keep getting 3x-1 outside and (x+1) and (x+2) on the inside. The polynomial is 3x^2+5x-2. Can you help me, please?

[minkusbc]

@valumni : 3x^2 + 5x - 2 (Multiply the 3 times the 2 to make 6. What multiplies to make 6 and subtracts to make +5 is +6 - 1.) We therefore now have the middle term expanded to two terms and we get 3x^2 + 6x - 1x - 2. Drop down the middle sign ( - ) and fact or each half independently and we get 3x ( x + 2) - 1( x+ 2). NOTICE the sign change in the second bracket. We now have our answer of (3x - 1) (x + 2). Hope this helps.

[kldudmp]

How would you work out: 6x^2+13x-8?

I'm really stuck on how to do it. Please help.

Thanks.

[minkusbc]

@kldudmp Multiply the 6 times the 8 to get 48, THen asks yourself "self, what multiplies to make 48 and SUBTRACTS to make 13?" (since the last term's sign is a minus sign, we subtract). THe answer is 16 and 3. Break the middle term up to 16x -3x and you now have 4 terms: 6x^2 + 16x - 3x - 8. Drop middle sign down and factor each half separately gives you 2x(3x + 8) - 1(3x + 8) (Factoring out a negative 1 changes the sign. Now factor common bracket to get (2x - 1)(3x + 8).

[ninjagoalie72]

what is 3x^2 - 14x - 5?

i tried using decomposition but i cant find a factor that mutiplies to 15 and subtracts to 14

[minkusbc]

@ninjagoalie72 : Hi Ninja: The answer is 1 and 15. They multiply to make 15 and subtract to make 1. Hence we write 3x^2 -1x +15x - 5. This equals x(3x - 1) + 5(3x - 1) or the answer of (x + 5)(3x - 1).

[BanglishBoy]

duude, you saved me for ma precal test, u the shit!

[635059462]

omg im in summer school and the teacher doesn't really teach that well >.>" only notes x-x and now with this i actually get it T^T ITS HELPS ME SO MUCH!!!

[oXPINKjellyBEANXo]

i really appreciate this video! thanks! :)

[CecyliaEJackson]

Can you please put a video on how to factor

15a^3 b^2-46a^2 b^3-60a^2b???

[dcn0007]

Thank you :) ,,, Helped me out big time

[kps1215]

i have a ? on my HW that I am totally stumped on: 6y`2 - 13y - 5. I did your triple play method and it came out to:

(6 y + 2) (6y - 15)

------------------------ 6

and neither side is divisible by 6!

Please help me! I'm desperate and this is literally the only ? i couldn't get using this method!!! am I doing something wrong, or do I have to do something differently to solve with - signs??

THANKS

[ReilaRyu9]

what happens if you get bigger numbers like 48x^2-200x+200?

[nastyNAS668]

can u please help me i have a test tmrw and i'm factoring..... 9xsquared-30xy+25ysquared

[MrArmm85]

i hate math!!

[valumni]

@minkusbc OH! I kept using 3 and 2 as the numbers to multiply 6 and add up to 5. I see. Thanks so much!