Question

Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown. Step 1: (6x4 – 8x2) + (3x2 + 4) Step 2: 2x2(3x2 – 4) + 1(3x2 + 4) Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?

Answer 1

Answer:

B. Faelyn should realize that her work shows that the polynomial is prime

Step-by-step explanation:

The polynomial 6x⁴ – 8x² + 3x² + 4 needs to be factored and the steps are:

Step 1: (6x⁴ – 8x²) + (3x² + 4)

Step 2: 2x²(3x² – 4) + 1(3x² + 4)

Since they do not have a common factor, Faelyn should realize that her work shows that the polynomial is prime. A prime polynomial cannot be factored further because it is at its lowest common term and cannot be factored into any other polynomial of a lower degree. Prime polynomials have integer coefficients. A prime polynomial is also referred to as an irreducible polynomial.