A number is called algebraic if there is a polynomial with rational coefficients for which the number is a root. For example, 2 is algebraic because it is a root of the polynomial x2−2. The number 2+3+5 is also algebraic because it is a root of a monic polynomial of degree 8, namely x8+ax7+bx6+cx5+dx4+ex3+fx2+gx+h. Find ∣a∣+∣b∣+∣c∣+∣d∣+∣e∣+∣f∣+∣g∣+∣h∣.
Details and assumptions:
A monic polynomial is a polynomial whose leading coefficient is 1.
For those who can't see the square roots clearly, the number is (2+321+521)21.
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