Cubic Equation

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October 22nd 2008, 10:23 PM
Kaynight

Cubic Equation

I know cubic equations must have the form $Ax^3 + Bx^2 + Cx + D = 0,$ and I know how to solve that type of equation by doing long division etc:

However I got this cubic question,

$x^3-3x^2+4$

It doesn't have the same form as above and it's put me right off knowing what to do. I tried to simplify it $( x(x^2+3x) +4)$ but I got no where fast. So any starters of where I should start to factorize would be very helpful!
October 22nd 2008, 11:30 PM
Laurent

Quote:

Originally Posted by Kaynight

I know cubic equations must have the form $Ax^3 + Bx^2 + Cx + D = 0,$ and I know how to solve that type of equation by doing long division etc:

However I got this cubic question,

$x^3-3x^2+4$

It doesn't have the same form as above and it's put me right off knowing what to do. I tried to simplify it $( x(x^2+3x) +4)$ but I got no where fast. So any starters of where I should start to factorize would be very helpful!

It has the same form as above, with $C=0$ .
You can notice that $-1$ is a solution, hence $x+1$ divides your polynomial. It remains to compute $Q(x)$ such that $x^3-3x^2+4=(x+1)Q(x)$ .
October 23rd 2008, 12:00 AM
Kaynight

Quote:

Originally Posted by Laurent

It has the same form as above, with $C=0$ .
You can notice that $-1$ is a solution, hence $x+1$ divides your polynomial. It remains to compute $Q(x)$ such that $x^3-3x^2+4=(x+1)Q(x)$ .

Many Thanks! :D

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