118k views
5 votes
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

1 Answer

5 votes

Answer:

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
User Supervacuo
by
4.7k points