C Chevy New member Joined Jul 20, 2007 Messages 4 Aug 25, 2007 #1 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.
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.
D Deleted member 4993 Guest Aug 25, 2007 #2 Re: I have completely forgotten how to factor cubic equation Chevy said: 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. Click to expand... 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.
Re: I have completely forgotten how to factor cubic equation Chevy said: 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. Click to expand... 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.
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Aug 25, 2007 #3 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: \(\displaystyle \L\\x(x^{2}+x+3)-2(x^{2}+x+3)\) \(\displaystyle \L\\\fbox{(x-2)(x^{2}+x+3)}\)
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: \(\displaystyle \L\\x(x^{2}+x+3)-2(x^{2}+x+3)\) \(\displaystyle \L\\\fbox{(x-2)(x^{2}+x+3)}\)
