Find the polynomial of minimal degree, in $x,$  which has rational coefficients, leading coefficient $1$, and roots $1+\sqrt{2}$ and $1+\sqrt{3}.$ (Write the terms in decreasing order of degree.)
Question:
Find the polynomial of minimal degree, in $x,$  which has rational coefficients, leading coefficient $1$, and roots $1+\sqrt{2}$ and $1+\sqrt{3}.$ (Write the terms in decreasing order of degree.)
Answer:
Let's think step by step.

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x^4-4x^3+x^2+6x+2
Find the polynomial of minimal degree, in $x,$  which has rational coefficients, leading coefficient $1$, and roots $1+\sqrt{2}$ and $1+\sqrt{3}.$ (Write the terms in decreasing order of degree.)
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