So how do you write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros with is problem: 5 and 4 + √2

Answer 1

irrational zeroes occur in conjugate pairs, so 4-√2 is also a root
(x-(4+√2))(x-(4-√2))(x-5)
= ((x-4)-√2)((x-4)+√2)(x-5)
= ((x-4)^2 - 2)(x-5)