alleryWhich first-degree polynomial is a factor of x⁵ − a⁵ for every value of a?
Ax − a
Bx² − a²
Cx + a
Dx − a²
Answer & Solution
Correct answer: A. x − a
1. The unit's 'Power difference' box states that x − a is a factor of xⁿ − aⁿ for every natural number n.
2. For n = 5 the result xⁿ − aⁿ = x⁵ − a⁵.
3. So x − a is the first-degree factor.
4. The general formula gives x⁵ − a⁵ = (x − a)(x⁴ + ax³ + a²x² + a³x + a⁴).
5. The other options are higher-degree or wrong-sign factors.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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