Problem 41 - Introductory Algebra for College Students

Question

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$11 x^{2}-23$$

Step-by-Step Solution

Answer

The given polynomial \(11x^{2}-23\) cannot be factored.

Step 1: Identify the GCF

The greatest common factor for \(11x^{2}\) and \(-23\) is 1, as there are no common factors that multiply to \(11x^{2}\) or \(-23\) apart from 1.

Step 2: Factorize the polynomial

Since the greatest common factor of both terms is only 1, this implies that the polynomial \(11x^{2}-23\) cannot be factored.