Algebra 2 Help...

[Rip the Jacker]

Can someone verify this? http://img114.imageshack.us/img114/1756/hw8cg.jpg

The problems I'm on:

Use synthetic division and the given factor to completely factor each polynomial function

y = x^3 + 3x^2 - 13x - 15; (x+5)

y = x^3 - 3x^2 -10x +24; (x-2)

Divide.

(6x^3 +2x^2 - 11x +12) / (3x+4)

(x^4 + 2x^3 + x -3) / (x-1)

(2x^4 + 3x^3 - 4x^2 + x + 1) / (2x-1)

(x^5 -1) / (x-1)

(x^4 - 3x^2 -10) / (x-2)

(3x^3 - 2x^2 +2x +1) / (x+1/3)

Last problem...

A box is to be mailed. The volume in cubic inches of the box can be expressed as the product of its three dimensions: V(x) = x^3 -16x^2 +79x -120. The length is x-8. Find linear expressions for the other dimensions. Assume that the width is greater than the height.

 

[Zim Hosein]

Did I do this right? If so what do I need to finish it off?

More handcream!

 

[Dissipate]

Just divide the original polynomial by the binomials and see if they divide evenly.

 

[JustAnAverageGuy]

Synthetic division FTW?

 

[Cattlegod]

Originally posted by: Zim Hosein

Did I do this right? If so what do I need to finish it off?

More handcream!

bahhahahahahah!!!!!!
hahahaha
!!!

 

[Dissipate]

Originally posted by: JustAnAverageGuy
Synthetic division FTW?

Yeppers. Good ole synthetic division. We re-visited that briefly in my abstract algebra class. W00t!

 

[Rip the Jacker]

So, can someone tell me if i did it right, and what i need to do now?

 

[JustAnAverageGuy]

If you get 0 at the end, it is a factor. If you don't, then it isn't.

Yes, that is my handwriting

Synthetic Division Pic

questions?

It can be further simplied to a product of linear factors (x+4)(x+2)(x-3) = x³ + 3x² -10x -24 in which case -4, -2, and 3 are all critical values (polynomial = 0)

 

[Rip the Jacker]

Ok. What factors are there for me to use synthetic vs long divison?

 

[Cooler]

Just plug in the numbers and if it ==0 then its a factor

x^3 + 3x^2 -10x -24 == 0

plug in for x
-4
3
-6
-2

 

[brainwrinkle]

Well, synthetic only works with a linear divisor (no x^2 or higher in the divisor), but it is much easier IMO. In other words, use it whenever possible.

 

[IAteYourMother]

it's MC, so for each answer there is a value of x that will give you 0 for the function
for a, f(-4)=0. See if that's true
etc etc

 

[IAteYourMother]

I highly suspect it's 1 or 3

 

[Rip the Jacker]

Ok. I think I'm alright with synthetic division now. How about long division?

(x^2 - 13x -48) / (x+3)

2x^2 + x 0 7 / (x-5)

(x^3 + 5x^2 -3x - 1) / (x-1)

(3x^3 -x^2 -7x + 6) / (x+2)

How would I do the first problem?

x+3|x^2-13x-48

 

[Goosemaster]

dude.....I psoted this in your other thread......you might try not abandoning it

 

[Rip the Jacker]

Originally posted by: Goosemaster
dude.....I psoted this in your other thread......you might try not abandoning it

Yeah, thank you for the first 4 problems. I've completed half the sheet now, and I'm on long division.

My other thread was turned into a ... "what math did you take in X year" thread..

 

[yosuke188]

I usually use long division. So many things can go wrong when using synthetic division like place holder, remembering it's not the negative and adding and it's just confusing.

 

[coomar]

Originally posted by: Dissipate

Originally posted by: JustAnAverageGuy
Synthetic division FTW?

Yeppers. Good ole synthetic division. We re-visited that briefly in my abstract algebra class. W00t!

don't you do polynomial division in grade 9-10, remainder theorem, factor theorem?

 

[Rip the Jacker]

Can someone verify this?

http://img114.imageshack.us/img114/1756/hw8cg.jpg

 

[Rip the Jacker]

ok. got the long division ones.

 

[Rip the Jacker]

up, new problems in OP

 

[Dissipate]

Originally posted by: coomar

Originally posted by: Dissipate

Originally posted by: JustAnAverageGuy
Synthetic division FTW?

Yeppers. Good ole synthetic division. We re-visited that briefly in my abstract algebra class. W00t!

don't you do polynomial division in grade 9-10, remainder theorem, factor theorem?

Yep. But this time we do it over other fields and we do things like reducibility tests.