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?

Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Faelyn should factor out a negative from one of the groups so the binomials will be the same.

Answer 1

An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.

What are prime polynomials?

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called a prime polynomials.

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 any common factor.

Faelyn should realize that her work indicates that the polynomial is prime.

Prime polynomials have integer coefficients.

An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.

Learn more about prime polynomials here:

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