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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.
Falyn should factor out a negative from one of the groups so the binomials will be the same.

Respuesta :

Answer:

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

Explanation:

The only difference between her factors in Step 2 is that the 4 in the first group is negative, while the 4 in the second group is positive.

Rearranging the polynomial to factor it will not change the end result.

Factoring out a negative will make not only one, but both terms, in one of the binomials the opposite sign; this will not make the factors the same.

Factoring only 2x out of the first group will result in having (3x³+4x); this is not the same either.

She should realize that when this happens, her polynomial is prime.

The precision of what Faelyn should do is that Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.

How to find the factors of polynomial?

Factors of the polynomial which are multiplied to produce the original polynomial.

The polynomial which can not be factored is known as prime polynomial.

The standard form of the polynomial with highest power of 2 can be given as,

Given information-

The given polynomial equitation in the problem is,

[tex]6x^4 -8x^2 + 3x^2 + 4[/tex]

  • 1) First step of Faelyn is

         [tex](6x^4- 8x^2) + (3x^2 + 4)[/tex]

  • 2) Second step of Faelyn is

       [tex]2x^2(3x^2 - 4) + 1(3x^2 + 4)[/tex]

Faelyn noticed that she does not have a common factor. The polynomial which can not be factored is known as prime polynomial.

Thus Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.

Learn more about the polynomial equation here;

https://brainly.com/question/2833285

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