Another algebra question

[iamaelephant]

Can anyone point me to an online lesson on factorising cubic polynomials such as

2x^3 + x^2 - 8x - 4

Would be very much appreciated, thanks!

 

[Fullmetal Chocobo]

Originally posted by: Falcon39
Can anyone point me to an online lesson on factorising cubic polynomials such as

2x^3 + x^2 - 8x - 4

Would be very much appreciated, thanks!

Homework FTL.
Google FTW.

 

[imported_Tick]

Use synthetic division. Google it to learn how.

 

[Dritnul]

i dunno but there is 3 possible answers i would just put it into my TI-86 and let that handle it then work the problem backwards

 

[iamaelephant]

Originally posted by: Dritnul
i dunno but there is 3 possible answers i would just put it into my TI-86 and let that handle it then work the problem backwards

I'm not after a solution, just need to know how to factorise it. Googling at the moment but there's not a lot of help there, seems most people are more concerned with solving the problem than factorising.

 

[esun]

2x^3 + x^2 - 8x - 4
= x^2(2x + 1) - 4(2x + 1)
= (2x + 1)(x^2 - 4)

Done. You can't do this with all cubic polynomials, naturally, but if they ask you to factor a cubic polynomial most likely it can be split in this fashion.

 

[IAteYourMother]

synthetic division ftw?

 

[iamaelephant]

Originally posted by: esun
2x^3 + x^2 - 8x - 4
= x^2(2x + 1) - 4(2x + 1)
= (2x + 1)(x^2 - 4)

Done. You can't do this with all cubic polynomials, naturally, but if they ask you to factor a cubic polynomial most likely it can be split in this fashion.

Ah excellent, thanks. The answer given in the Answers section was (2x+1)(x+2)(x-2) so you're dead right. To the guys suggesting synthetic division, your help is much appreciated but it seems from a quick Google search that synthetic division is used to solve the problem rather than factorising it.

This forum is excellent for homework help!

 

[chuckywang]

Originally posted by: Falcon39
Can anyone point me to an online lesson on factorising cubic polynomials such as

2x^3 + x^2 - 8x - 4

Would be very much appreciated, thanks!

It's obvious by inspection that x=2 is a root, so x-2 is a factor. Divide the polynomial by (x-2) and then find the roots of the resulting quadratic.

There is no real way to factor a general cubic without remembering the long formula for the roots of a cubic. There are some tricks to quickly determine if an integer is a root or not, but that's about it. In this case, you can do it by inspection.