Question 1156234
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The answer to the problem in the post by @josgarithmetic  IS  NOT  CORRECT.


The correct answer is  THIS:


<pre>
    This polynomial of the degree 6 has 6 real roots:


       {{{-sqrt(2)}}}, -1, 0 of the multiplicity 2, 1, and {{{sqrt(2)}}}.


    All its roots are real numbers.


    The correct factoring into the product of 6 binomials is

        p(x) = {{{x^2*(x-1)*(x+1)*(x-sqrt(2))*(x+sqrt(2))}}}.
</pre>