Question

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

If Faelyn found no common factor in a polynomial, regrouping the terms or factoring out a negative could help. If these strategies do not work, it might mean the polynomial is prime. Always simplify the algebra where possible and verify the solution.

Step-by-step explanation:

If Faelyn noticed that she does not have a common factor when factoring a polynomial, it might be useful for her to go back and regroup the terms. For instance, regrouping the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4) might reveal a common factor that was not initially apparent. If after regrouping the terms, a common factor is found, she can then proceed to factor it out, otherwise, she may realize that the polynomial is prime and not factorable. Another strategy could be to factor out a negative from one of the groups so the binomials will be the same, which is essential for the factoring by grouping method.

If no common factor or strategy leads to further simplification, it is important to eliminate terms wherever possible to simplify the algebra. Ultimately, the solution should be verified to check if it is reasonable, ensuring that all steps were correctly followed.

Answer 2

Without knowing what Faelyn has done so far or what she is working with, the second selection seems appropriate.

6x^4 -5x^2 -4
= (6x^4 +3x^2) -(8x^2 +4)
= 3x^2*(2x^2 +1) -4(2x^2 +1)
= (3x^2 -4)(2x^2 +1)