Question

Which polynomial is prime?

A) x + 3x² - 2x - 6
B) x² - 2x² + 3x - 6
C) 44A + 4x² - 2x - 2
D) 2xA + x² = x + 2

Answer 1

The prime polynomial is Option B: x² - 2x² + 3x - 6.

Step-by-step explanation:

A polynomial is considered prime if it cannot be factored into two or more polynomials with integer coefficients.

Let's analyze each of the given options:

• Option A: x + 3x² - 2x - 6 = 3x² - x - 6, which can be factored as (3x + 2)(x - 3). Therefore, this polynomial is not prime.
• Option B: x² - 2x² + 3x - 6 = -x² + 3x - 6, which cannot be factored further. Therefore, this polynomial is prime.
• Option C: 44A + 4x² - 2x - 2 is not a valid polynomial expression due to the presence of 'A'.
• Option D: 2xA + x² = x + 2 = x² + (2 - x)(x + 1), which can be factored. Therefore, this polynomial is not prime.

Based on the analysis, Option B is the only prime polynomial.