Question

Which polynomial is prime? A. x^4 + 3x^2 – x^2 – 3 B. x^4 – 3x^2 – x^2 + 3 C. 3x^2 + x – 6x – 2 D. 3x^2 + x – 6x + 3

Answer 1

A and B

Explanation:

• A polynomial with integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients, is called an irreducible or prime polynomial

As per above definition, A and B polynomials have coefficients 1 or 3, so are prime polynomials.

C and D polynomials have coefficient of 6 which can be further factored

A. x^4 + 3x^2 – x^2 – 3

• yes

B. x^4 – 3x^2 – x^2 + 3

• yes

C. 3x^2 + x – 6x – 2

• no

D. 3x^2 + x – 6x + 3

• no