Question

Hey guys!!
While using synthetic division,wat are the best(most apt) numbers to use to get the first factor out by trial and error??

Answer 1

Do you remember how to list the possible factors of a polynomial?
That would be the list I would pull from

Answer 2

So, the combination of a graph of the function, and that list of possible roots
It's not a simple answer :)

Answer 3

I just did--kind of gave you the answer :)
I meant that it isn't a one word answer
So, the combination of a graph of the function, and that list of possible roots

Answer 4

Not gtin u ....@Tutor.Stacey .....can u elaborate a bit??

Answer 5

Here is a website which I have found helpful in the past: http://www.purplemath.com/modules/synthdiv.htm. Hopefully it can help a bit :)

Answer 6

URL > http://www.purplemath.com/index.htm
ah--that's didn't work--tried to pull up an example for you same here

Answer 7

Oh dear, thanks

Answer 8

and the factors of the leading coefficient
(in this case, factors of 12 and 1)
And make ratios out of them
Those are the possible factors of the polynomials

Answer 9

Then you make a graph of the function and see which of the possible values might be roots
Then you use one of those numbers for synthetic division
That's about as specific as I can get--we can work through an example if you would like

Answer 10

K...how bout x^3+x^2+2x-4=0??

Answer 11

So, let's list the factors of the constant term first
What is the constant term here?

Answer 12

@Incognito!!Ur link is a 404 error!!

Answer 13

-4

Answer 14

@cambrige Actually, this one is really easy--just try graphing the function ;)
And yes---4!

Answer 15

And then you want to list the factors of -4

Answer 16

Well...U always kinda dont hve the time for graphing....any alternative
??

Answer 17

Let's keep working through this so you see how it works...
what are the factors of 4?

Answer 18

1,2,4

Answer 19

Ya take ur time............
Hurry back..........Just kiddin @Tutor.Stacey !!

Answer 20

From here, you make ratios of all of these--that gives you a total of 12 possible rational roots
So, from there, graphing really is the only
*way

Answer 21

If you have a graphing calcuator, I would graph with that
If not, then you can try a few values by hand

Answer 22

Just to see what the general shape of the graph is

Answer 23

RAtios wrt what??

Answer 24

Can u give an example!!*.*

Answer 25

Sorry, this is really complex and it takes sometime to fully understand.

Answer 26

Just to see what's happening
Do you have access to a graphing calculator for this type of question?

Answer 27

So...
1/1, 2/1, 4/1, -1/1, -2/1, -4/1
And then do the same with -1
1/-1, 2/-1, 4/-1, -1/-1, -2/-1, -4/-1

Answer 28

Those are all the roots
Obviously, some of them are repeats: -4/-1 and 4/1 are the same (4)

Answer 29

Whoa!!..kinda gtin it!

Answer 30

ok good!

Answer 31

So those are all the choices
There are lots of them

Answer 32

So how to find wich of'em work??....Acubic can at max hav three,r8??i.e 3 roots

Answer 33

Yes...so we need to graph
Do you have a calculator or are we doing this by hand?

Answer 34

Hand pls.....old school!!

Answer 35

ok sure...

Answer 36

okay--so let's plug in -1 into the function

Answer 37

Not gtin,I guess!!

Answer 38

okay--so let's plug in -1 into the function
(-1)^3 + (-1)^2 + 2(-1) - 4
What do you get?

Answer 39

are you ok with that so far?

Answer 40

-6

Answer 41

which bit don't you understand?

Answer 42

ya...cntnu!!

Answer 43

look, If you don't have a calculator, we need to find the shape of the graph by hand
To do this, we need to find what the graph looks like
We need to plug in various values for x to find out a few points on the graph
So we are plugging -1, 0 and 1 in for x

Answer 44

You simply replace x with -1
(-1)^3 + (-1)^2 + 2(-1) - 4
Then you need to work through that to find what the y-value is

Answer 45

Can you try this?

Answer 46

break it down, so, what is (-1)^3?

Answer 47

that = -1

Answer 48

So -1 + (-1)^2
What is (-1)^2

Answer 49

I already posted the y value as -6 a couple of posts back!!

Answer 50

that = 1

Answer 51

oh, i see.

Answer 52

so I get (-1,-6) & (0,-4)

Answer 53

Good!

Answer 54

Good!
Let's try one more value!
It looks like we are getting closer to the x-axis, right?

Answer 55

tnx

Answer 56

yes

Answer 57

no problems.

Answer 58

I just want to make sure you understand this, so there is no more confusion.

Answer 59

So now (1)^3 + (1)^2 + 2(1) - 4

Answer 60

Ya, m going wid the flow!!

Answer 61

we get (1,0)

Answer 62

so x-1 is a factor,eh??

Answer 63

Yay!

Answer 64

So, 1 is a root!
So that is what we should use for synthetic division

Answer 65

ok.........Loved ur effort.....WElcome to OS..and tnx for the help!!
And also to all others!!

Answer 66

We got lucky there, but, if nothing else, this will help you get a better guess :)

Answer 67

hmmm....Aye aye tutor!!

Answer 68

http://openstudy.com/users/nylejre#/updates/51ff80c5e4b05ca7841fe68c

Answer 69

You're welcome--is that all you needed?
Or did you need to factor the polynomial completely?

Answer 70

Check this post....wanna help??

Answer 71

sure

Answer 72

No I can do dat....Doubt Cleared.....!!!

Answer 73

haha, that is good to hear. One moment let me take a break.

Answer 74

at least you clearly understood the concept, I'm glad.

Answer 75

Me too!!

Answer 76

Ya u do dat!!Doubts await u wen u cum back!!

Answer 77

Ok. I'm glad you liked my assistance...

Answer 78

Loved it..

Answer 79

k gtg...some calc problems await me.so long!!

Answer 80

I'll be offline soon.

Answer 81

Okay, take care and if you need any further help feel free