If α and β are the roots of the equation $3x^2+5x+4=0$, find the value of $α^3+β^3$ If α and β are the roots of the equation $3x^2+5x+4=0$, find the value of $α^3+β^3$
How can I factorize the expression to use the rule of sum and product of roots?
The answer is $\frac{55}{27}$

Vieta's theorem is the key, like in your previous question. It gives $\alpha+\beta=-\frac{5}{3}$ with no effort and 
$$\alpha^3+\beta^3 = (\alpha+\beta)\left((\alpha+\beta)^2-3\alpha\beta\right) = -\frac{5}{3}\left(\frac{25}{9}-4\right) = \color{red}{\frac{55}{27}}$$
with very simple manipulations.
