Question

pls help!

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: (6x^4 – 8x^2) + (3x^2 + 4)

Step 2: 2x^2(3x^2 – 4) + 1(3x^2 + 4)

Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?

Answer 1

HI!!

Answer 2

is this
\[6x^4-8x^2+3x^2+4\]?

Answer 3

yes

Answer 4

it is the same as
\[6x^4-5x^2+4\] when you combine like terms

Answer 5

yup

Answer 6

but it does not factor, so the question "what should Faelyn do next" has not real answer other than "go have a beer"

Answer 7

not sure what the options are
looks like you were given choices

Answer 8

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

Answer 9

hmm not really clear
probably the first one, because it is prime
but that is not a proof that it is prime
we can check the other ones

Answer 10

b) Faelyn should go back and regroup the terms in Step 1 as (6x^4 + 3x^2) – (8x^2 + 4).
this does not help

Answer 11

c) In Step 2, Faelyn should factor only 2x out of the first expression.
this does not help either

Answer 12

d) Faelyn should factor out a negative from one of the groups so the binomials will be the same
this is wrong as well,

not really clear
it is prime, so no matter what you do you will not be able to factor it

Answer 13

this is the problem

Answer 14

it still does not factor

Answer 15

no matter what you do
might as well throw in the towel

Answer 16

oh i got it, tnx

Answer 17

its prime

Answer 18

actually we can combine like terms for the x^2 part making the equation
\[6x^4-5x^2+4\]
now we can factor if and only if we have a perfect square result from the discriminant formula
which is
\[b^2-4ac\]
so letting b = -5,a = 6, and c = 4

\[(-5)^2-4(6)(4)\]
\[25-96 = -71\]
not a perfect square so this quadratic equation can't be factored. The quadratic formula needs to be used, but it's not asking to solve further in this question. So, this is a prime polynomial because in the discriminant we had -71. the number 71 is indeed a prime number. However, taking the square root of -71 we have \[\sqrt{71}i\]. since negative numbers aren't allowed in the radical the result is imaginary or i.
all the roots for this equation is complex.

Answer 19

sorry only saw earlier post when the equation wasn't combined for the first line of my comment