Question

Which polynomial is prime?

A) 31 + 372 - 2x - 2
B) 31 - 212 + 3x - 4
C) 4 + 212 + 6x + 3
D) 4 + 4² - 3x - 3

Answer 1

The prime polynomial among the given options is 4 + 212 + 6x + 3.

Step-by-step explanation:

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

Let's analyze each option:

• A) 31 + 372 - 2x - 2: This polynomial can be simplified to 401 - 2x, but it can still be factored into 1(401 - 2x), so it is not prime.
• B) 31 - 212 + 3x - 4: This polynomial can be simplified to -175 + 3x, but it can still be factored into -1(175 - 3x), so it is not prime.
• C) 4 + 212 + 6x + 3: This polynomial cannot be simplified further and does not have any factors other than 1 and itself, so it is prime.
• D) 4 + 4² - 3x - 3: This polynomial can be simplified to 25 - 3x, but it can still be factored into 1(25 - 3x), so it is not prime.

Therefore, the only prime polynomial among the given options is C) 4 + 212 + 6x + 3.