Home › Kerala SSLC (Class 10) › mathematics › Polynomials › Which first-degree polynomial is a factor of x⁵ …
Which first-degree polynomial is a factor of x⁵ − a⁵ for every value of a?
Answer & Solution
Correct answer: 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.)._
Related questions
Given any polynomial p(x) and any number a, which polynomial is always a factor of p(x) − Which of the following second-degree polynomials cannot be factored into first-degree realThe factorization of 2x² − 7x + 6 into first-degree polynomials is:In the polynomial x² + kx + 6, the value of k that makes x − 1 a factor is:The polynomial x² + 1 has no first-degree factors over the real numbers because:Using the quadratic formula, the solutions of x² − 30x + 221 = 0 are:If p(x) is a polynomial and p(a) = 0 for some number a, then which first-degree polynomialThe solutions of the equation x² + 2x − 15 = 0 are: