Answer:
[tex]x^3-10x^2+31x-28[/tex]
Step-by-step explanation:
Since we are looking for a polynomial with RATIONAL coefficients, then we know that if [tex]3-\sqrt{2}[/tex] is a root, then its conjugate [tex]3+\sqrt{2}[/tex] must also be a root
Therefore, we build the polynomial using binomial factors with the given roots as shown below:
[tex](x-4)*(x-3+\sqrt{2} )*(x-3-\sqrt{2} )= (x-4)((x-3)^2-2)=\\=(x-4)*(x^2-6x+9-2) =(x-4)*(x^2-6x+7)=\\=x^3-10x^2+31x-28[/tex]
