Factoring polynomial

[soccerdude21490]

Hey I have a problem that I need to solve...

f(x)=x^5+x^2-10x-6


I've tried everything I can think of. I need to sovle this problem and then graph it for a project for Algebra II... anybody help?

 

[jsbeckton]

Its been a while since I've done these but think that you need to find all of the factors of the cooeficient of thelast term (6) and divide by the factors of the cooeficient of the first term (1)

\(\displaystyle \frac{{ \pm 1 \pm 2 \pm 3 \pm 6}}{{ \pm 1}}\)

so you have these possible factors:

1,2,3,6 (plus and minus all terms)

You need to pick one and use that division technique, I hope you know it because its kinda hard to explain in words. If say you pick 2 and do the division and end up with 0, then (x-2) is a factor, then you can continue until you have a polynomial that you can solve.

 

[Unco]

f(x) = x^5 + x^2 - 10x - 6 doesn't have any rational roots (it can't be factorised).

You could try your hand at numerical methods (eg. Newton-Raphson, Bisection) to find the roots.

If that's beyond Algebra II (I haven't a clue): apart from checking there isn't a typo, I'm out of ideas . . .

Edit: Josh, one only has to test f(-2) to see if (x + 2) is a factor; long division is a pain when you discover at the end your factor isn't a factor after all.

 

[jsbeckton]

One "trick" is to graph the polynomial and see where it crosses the x axis, then pick those numbers, but Unco is right, this has no rational roots and since you are only in Algebra II, I think that there must be a typo or your teacher dosen't like you very much! They usually give you nice numbers to work with.

 

[jsbeckton]

I know that you could simply check f(-2) but the key here is to find all of the factors and if you use long division (it can certainally be a pain) , you usually get a simple quadratic after you find the first root. I remember doing this in Algebra II and I think that the purpose of this assignment is to lean long division, not to find the factors, but I could be wrong.

 

[soccerdude21490]

alright yea, I think he might just want us to make a table of values and just graph it. Thanks a lot guys!

 

[stapel]

I need to sovle this problem and then graph it...

To "solve" this, you'll need to set the function (the polynomial) equal to something. Other posters have assumed that you meant "solve for the zeroes of the polynomial."

...he might just want us to make a table of values and just graph it.

This is why it is helpful to include the complete text of the exercise, including the instructions.

Just FYI.... :wink:

Eliz.