College Algebra?

Question

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

3 minus the square root of 3, 1 + 1

Please show your work. Thanks.

Answer 1

I'm not sure what the last 1+1 means but if it's one and negative one this is how you do it.
(x-(3sqrt(3))(x+1)(x-1)
Then you need to multiply this out which should be simple arithmatic.

Answer 2

If you have given the roots 3-sqrt(3), 1, and -1. One such polynomial function of lowest degree with rational coefficients is:
(x-3+sqrt(3))(x-3-sqrt(3))(x+1)(x-1)
= [(x-3)^2 - 3](x^2-1)
= (x^2 - 6x + 6)(x^2-1)
= x^4 - 6x^3 + 5x^2 + 6x - 6