Question

Let \( f(x) = (x^5 - 1)(x^3 + 1) \), \( g(x) = (x^2 - 1)(x^2 - x + 1) \) and let \( h(x) \) be such that \( f(x) = g(x)h(x) \). Then

• A. 0
• B. 1
• C. \( 2 \)
• D. \( 3 \)

Hint:

When solving for unknown functions in equations involving products, factor the given functions and solve accordingly.

Answer 1

The Correct Option is D

Step 1: Express the functions and solve.
The given equation is \( f(x) = g(x)h(x) \), and solving for \( h(x) \) involves algebraic manipulation of the terms.
Step 2: Conclusion.
We find that \( h(x) = 3 \). Final Answer: \[ \boxed{3} \]