Question

The degree of the polynomial \( \left( x + \sqrt{x^4 - 1} \right)^9 + \left( x - \sqrt{x^4 - 1} \right)^9 \) is:

• A. 14
• B. 15
• C. 16
• D. 17

Hint:

When dealing with sums of polynomials, consider the highest degree term from each part of the sum.

Answer 1

The Correct Option is D

The given polynomial is of the form \( \left( x + \sqrt{x^4 - 1} \right)^9 + \left( x - \sqrt{x^4 - 1} \right)^9 \). The degree of each term is determined by the highest power of \( x \) in the expansion of each binomial. Since we are dealing with terms of degree 9 in the expansions of both polynomials, the degree of the resulting polynomial is \( 17 \) after combining terms.