Question

Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.

Answer 1

It is hard to say how Faelyn's work shows the polynomial is prime, but it is.

There are no factors of 6*4 = 24 that add to -5, so the polynomial cannot be factored using real numbers.
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The expression of suggestion 2 is a different polynomial than the one Faelyn is factoring.
Taking a factor of 2x out of the first group does not help it match the factoring of the second group.
Dividing one or the other of the groups by -1 will not make the binomials the same.

Answer 2

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.