I have completely forgotten how to factor cubic equations.

[Chevy]

I have been looking all over and found the grouping method. But that doesn't solve the problem i just ran across:

x^3-x^2+x-6

So, I can't remember at all how to do this, so I need help.

Thanks.

 

[Deleted member 4993]

Re: I have completely forgotten how to factor cubic equation

I have been looking all over and found the grouping method. But that doesn't solve the problem i just ran across:

x^3-x^2+x-6

So, I can't remember at all how to do this, so I need help.

Thanks.

There are very complicated rules for factoring cubic functions.

My favorite rule is - graph it and you'll find the zeros - thn factor those out. For example this function has a real zero at x = 2.

So (x-2) is a factor.

You can divide that out - then you'll be left with a quadratic. That you can factor easily.

 

[galactus]

With this one, you could try some gymnastics and group.

Rewrite as:

\(\displaystyle \L\\x^{3}+x^{2}-2x^{2}+3x-2x-6\)

Group:

\(\displaystyle \L\\(x^{3}+x^{2}+3x)-(2x^{2}+2x+6)\)

Factor:

\(\displaystyle \L\\x(x^{2}+x+3)-2(x^{2}+x+3)\)

\(\displaystyle \L\\\fbox{(x-2)(x^{2}+x+3)}\)