Cubic Equation

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


However I got this cubic question,


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


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 $\displaystyle ( x(x^2+3x) +4)$ but I got no where fast. So any starters of where I should start to factorize would be very helpful!

Quote:

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Originally Posted by Kaynight

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


However I got this cubic question,


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


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 $\displaystyle ( x(x^2+3x) +4)$ but I got no where fast. So any starters of where I should start to factorize would be very helpful!

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

Quote:

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Originally Posted by Laurent

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

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Many Thanks! :D