Question

Hey guys, I'm really confused on this question. I tried factoring it with synthetic division with no luck, and to be honest I'm not very good with factoring it from scratch (As it was not even taught this way in this unit) So help and explanation would be appreciated.
Factor completely: x^5+x^4-13x^3 - 13x^2 + 36x - 36
Thanks!

Answer 1

I think that you have to start by trying a number for x and see if it is too low or high..That is always an option

Answer 2

Are you missing any extra variables or have you labeled any of the exponents incorrectly?

Answer 3

because if so that might be why this problem is not making as much sense because it seems to me that there would have to be a missing variable or a miss placed exponent.

Answer 4

Also, is there an answer?

Answer 5

Well, I just checked and this is how the problem is laid out.. I do believe this has something to do with something like x(x^4) or something. There are no answer choices: I'm expected to show my work.

Answer 6

..I'm at a loss on how to factor any of this o.o

Answer 7

so the last number does not have a variable? and the second 13x does not have the same exponent?

Answer 8

No, because this equation is mostly ready for synthetic division. However, I did synthetic division with factors of -36 with no luck with any of the numbers.

Answer 9

Look on purple math.com you may be able to find an example of this problem. if you do post it and then i will attempt to help you again. I will think over the problem as you are doing this.

Answer 10

Unfortunately I have already tried searching on purplemath. If that is all you are able to do, I thank you for taking the time to try to help me. :)

Answer 11

this has one real root , only one

Answer 12

one nonrational real root
x = 3.357405080

Answer 13

Oh I found that on my graphing calc. Is there any way to show the work for finding that root, or is it only possible by graphing?

Answer 14

And do you know of a way to factor the equation?

Answer 15

only possible by graphing or using some kind of root finding method, like newtons method.

Answer 16

sorry I wasn't able to offer much help, but this one has really stumped me :(

Answer 17

not possible to find it by checking the rational roots

Answer 18

Thanks perl! And huntergirl it's perfectly fine, it stumped me really badly T_T Thanks for trying to help!

Answer 19

there is probably a typo

Answer 20

if you change that last -36 to positive 36

Answer 21

Oh so it's not factorable is what you're saying?

Answer 22

Thats what i figured @perl because it would make more since if there were common factors that you could cancel out in order to find the correct answer to this problem

Answer 23

$$
\Large{ factor(x^5+x^4-13*x^3-13*x^2+36*x\color{red}+36);
\\~~~~~~~~~~~~~~~~~~~~~ (x - 2) (x - 3) (x + 3) (x + 2) (x + 1)
}
$$

Answer 24

So if the constant is negative in this equation, the equation is not factorable?

Answer 25

correct , thats why theres probably a typo

Answer 26

That sounds about right but dang i don't think I have ever come across a problem like this one.

Answer 27

Ahh I'm thinking my teachers put in a trick question then. The test says the constant is subtracted. Trust me, I haven't either hunter xD So confusing >_< Thanks so much perl!! And thanks for the help too hunter!

Answer 28

Wait.. it does factor, or are you talking about when the constant is positive?

Answer 29

i mean when the constant is positive, it factors nicely

Answer 30

Ah ok, thanks so much perl!

Answer 31

thats why i suspect its a copying error

Answer 32

my mind is blown X_X

Answer 33

Same xD

Answer 34

A random quintic (fifth degree polynomial) that you can think of is not usually factorable.
Try to factor
x^5 + 4x^3 + 3x^2 - 20x + 1 (i just randomly picked that polynomial)

Answer 35

the first thing i would do would be to factor out the x but there is no x on the very last number of your problem i guess i am still confused...

Answer 36

because the mistake is just a sign, its probably a typo