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If n is the degree of the polynomial, [ 1 / (√(5x³ + 1) − √(5x³ − 1)) ]⁸ + [ 1 / (√(5x³ + 1) + √(5x³ − 1)) ]⁸ and m is the coefficient of xⁿ 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 xⁿ, which is 12, is found to be (8)(10)⁴ after evaluating the contributions from both terms in the expression.

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