# How do you write a polynomial function of least degree that has real coefficients, the following given zeros:  1, 1+sqrt(2), 1-sqrt(2)?

${x}^{3} - 3 {x}^{2} + x + 1$
$\left(x - 1 - \sqrt{2}\right) \left(x - 1 + \sqrt{2}\right) \left(x - 1\right) = \left({\left(x - 1\right)}^{2} - 2\right) \left(x - 1\right)$
$= {x}^{3} - 3 {x}^{2} + x + 1$