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If the roots to such a polynomial are 2 and 
, then we can write it as
courtesy of the fundamental theorem of algebra. Now expanding yields
which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.
So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use
as a root. In this case, that would make our polynomial
so that the answer is (probably) the third choice.
Whoever originally wrote this question should reevaluate their word choice...
courtesy of the fundamental theorem of algebra. Now expanding yields
which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.
So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use
so that the answer is (probably) the third choice.
Whoever originally wrote this question should reevaluate their word choice...