I'm totally confused!

**tpoma** · December 15th 2008, 09:21 AM

I am so confused on these!!

I get stated and then don't know where to start and where to end. Please help.

6a-3a^2-2ab+a^2b

I started with 3(3a-a^2) but not even sure if that is correct.

Thank you

**running-gag** · December 15th 2008, 09:34 AM

Hi

$6a-3a^2-2ab+a^2b = 2a(3-b)+a^2(b-3) = (a^2-2a)(b-3) = a(a-2)(b-3)$

**masters** · December 15th 2008, 09:35 AM

Originally Posted by tpoma

I am so confused on these!!

I get stated and then don't know where to start and where to end. Please help.

6a-3a^2-2ab+a^2b

I started with 3(3a-a^2) but not even sure if that is correct.

Thank you

First, factor out an a, then try gouping the terms when you have a 4-term polynomial.

Group the first 2, then the second 2 and pull out common factors.

$6a-3a^2-2ab+a^2b$

$a(6-3a-2b+ab)$

$a [ (6-3a)-(2b-ab) ]$

$a [ 3(2-a)-b(2-a) ]$

How's this working out for you? Can you finish up?

I'll finish up since running-gag had a slightly different approach

$a(2-a)(3-b) \ \ or \ \ a(a-2)(b-3)$

**tpoma** · December 15th 2008, 10:42 AM

Ok, I am trying this again, can you please tell me if this is correct or anywhere close to what I am trying to accomplish? Thanks

4k-8-k^3+2k^2

I have come up with 2k(2+k^2+2k) I don't feel confident that it is anywhere close to what I am suppose to have.

**running-gag** · December 15th 2008, 11:39 AM

No

$4k-8-k^3+2k^2 = 4(k-2) - k^2(k-2) = (4 - k^2)(k-2)$

$4k-8-k^3+2k^2 = (2+k)(2-k)(k-2) = -(k+2)(k-2)^2$

**tpoma** · December 15th 2008, 01:12 PM

Quick question,

On this problem why is it that the 9 seems to disapear? It seems to just drop off????

2y^3-18y^2= -28y

My final answer was 2y(y-2)(y-7)=0
2y=0 y-2=0
y=0 y=2

y-7=0 y=7
Where did the 9 go to?? I don't understand it but I think I got it right.

Thanks

**masters** · December 15th 2008, 01:49 PM

Originally Posted by tpoma

Quick question,

On this problem why is it that the 9 seems to disapear? It seems to just drop off????

2y^3-18y^2= -28y

My final answer was 2y(y-2)(y-7)=0
2y=0 y-2=0
y=0 y=2

y-7=0 y=7
Where did the 9 go to?? I don't understand it but I think I got it right.

Thanks

Your answers are correct. y = {0, 2, 7}

Here's how it goes:

$2y^3-18y^2=-28y$

$2y^3-18y^2+28y=0$

$2y(y^2-9y+14)=0$

When you factor the trinomial, the sum of the two factors that make 14 must add to make -9.

$2y(y-7)(y-2)=0$

You see. The -9y is made up of -7y + -2y. You may see it better this way.

$2y(y^2-7y-2y+14)=0$

Here, I just replaced the -9y in the middle with the sum of the two factors that made +14. Now, if I group the 4 term polynomial, I arrive at the desired factored result.

$2y[(y^2-7y)-(2y-14)]$

$2y[y(y-7)-2(y-7)]$

$2y(y-7)(y-2)=0$

$2y=0 \ \ or \ \ y-7=0 \ \ or \ \ y-2=0$

$y=0 \ \ or \ \ y=7 \ \ or \ \ y=2$

**tpoma** · December 15th 2008, 01:58 PM

ahhhh got ya, so I could have used FOIL on this problem once I got the equation set up....didn't even see it in a FOIL format! Thank you for your explination! They always seem to help when I am having problems!!

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