Find a monic quartic polynomial f(x) with rational coefficients whose roots include \(x=1-\sqrt2\) and \(x=2+\sqrt5\). Give your answer in expanded form.
There will be two more roots which are the conjugates of the given roots.
f(x) = [ x - (1 - sqrt(2) ] · [ x - (1 + sqrt(2) ] · [ x - (2 + sqrt(5) ] · [ x - (2 - sqrt(5) ]
Can you do the expanding?