# Factoring completely are we on the right track????

G

#### Guest

##### Guest
#1. 3Y^3 - Y^2 -21Y +7
(3Y^3-Y^2) -(21Y +7)
y^2(3Y -1) -7(3Y -1)

#2. T^3 -T^2- 16T +16
(T^3-T^2)-(16T-16)
T^2 (T-1) - 16(T-1)
T^2-16 (T+1)^2
(T-4)^2(T-1)^2

I hope you can understand what I mean...is my son on the right track with #!... and did he try too much on #2? Thanks for the help...this is what my son has for work on his paper and we plan on going over it tomorrow morning about 6:30 am but I'm not sure if he's got the right idea or not. And don't want to mess him up if he's right! All the reat of his assingment seem right but thiese were the 2 hardest problems... thanks for any and all help! Mom :?

G

#### Guest

##### Guest
Freshman in high School!

Will keep working! These 2 are the challenging problems of the assingment! Thanks for the link to help! Mom

#### Denis

##### Senior Member
Sorry mom, but both are hopelessly wrong...

All I can suggest is go here:
http://library.thinkquest.org/C0110248/ ... biceqn.htm

Factoring cubic equations is fairly advanced stuff.

Cubics work a bit like this:
(x-1)(x-2)(x-3)
Multiplying that out gives: x^3 - 6x^2 + 8x - 6

So if asked to factor x^3 - 6x^2 + 8x - 6, answer is:
(x-1)(x-2)(x-3)

The answer to your son's 2 problems will be a bit similar to that.
The 1st one: #1. 3Y^3 - Y^2 -21Y +7
will end up something like this:
(3x ???)(x ???)(x ???)

However, impossible to teach such a topic here...

EDIT: whoops, I must have it the "submit key" twice! :shock:

G

#### Guest

##### Guest
for #2 ..I get (T^2 +16)(T-1)(T+1)

But I keep wanting to simplify (T^2+16) ????

G

#### Guest

##### Guest
For #1 I get (Y^2-7)(3Y-1)(-3Y+1)

Am I getting any closer????

G

#### Guest

##### Guest
think I actually got it!!!!

When I multiply these 2 answers I actualy get what I started with...
I got
(Y2-7)(3Y-1) is that right???

#### TchrQbic

##### Junior Member
Re: think I actually got it!!!!

4 little piggies mom said:
When I multiply these 2 answers I actualy get what I started with...
I got
(Y2-7)(3Y-1) is that right???
#1 is correct, if written as (y^2 - 7)(3y - 1).

The second one has an error in factoring. (T^2 - 16) does not factor into (T - 4)^2. Try again.

#### Denis

##### Senior Member
Re: think I actually got it!!!!

TchrQbic said:
4 little piggies mom said:
When I multiply these 2 answers I actualy get what I started with...
I got
(Y2-7)(3Y-1) is that right???
#1 is correct, if written as (y^2 - 7)(3y - 1).
TchrQbic, should that not be (y + sqrt(7))(y - sqrt(7))(3y - 1) ?
Always thought that factoring a cubic ended with (?)(?)(?)

#### TchrQbic

##### Junior Member
Re: think I actually got it!!!!

Denis said:
TchrQbic said:
4 little piggies mom said:
When I multiply these 2 answers I actualy get what I started with...
I got
(Y2-7)(3Y-1) is that right???
#1 is correct, if written as (y^2 - 7)(3y - 1).
TchrQbic, should that not be (y + sqrt(7))(y - sqrt(7))(3y - 1) ?
Always thought that factoring a cubic ended with (?)(?)(?)
Of course you are right. On paper I make far fewer mistakes. :^(