Find all three roots of the cubic: 2x^3 +5x^2 - 22x +15=0.

First try a trivial solution, x=0: doesn't work. Then try x=1 this does work so (x-1) is a factor of the cubic. Through algebraic factorisation (2x²+7x-15) comes out as a factor. This can be factorised into (2x-3)(x+5) leaving x=1, x=3/2 and x=-5 as the three solutions.