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If n is the degree of the polynomial, [ 1 / (√(5x^3 + 1) − √(5x^3 − 1)) ]^8 + [ 1 / (√(5x^3 + 1) + √(5x^3 − 1)) ]^8 and m is the coefficient of x^n in it, then the ordered pair (n, m) is equal to

1. (12, (20)^4)
2. (8, (5)(10)^4)
3. (24, (10)^8)
4. (12, (8)(10)^4)

Correct answer: (12, (8)(10)^4)

Solution

The degree of the polynomial is determined by the highest power of x present, which is 12 in this case, as the expression simplifies to a polynomial of degree 12. The coefficient of x^n, which is 12, is found to be (8)(10)^4 after evaluating the contributions from both terms in the expression.

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