Hey I need some help with this problem

Factor the polynomial x^8-98x^4+1 into two non-constant polynomials with

integral coefficients.

I want to see steps on how to do this problem thanks.

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- Nov 10th 2012, 09:26 PMgfbrdFactoring help
Hey I need some help with this problem

Factor the polynomial x^8-98x^4+1 into two non-constant polynomials with

integral coefficients.

I want to see steps on how to do this problem thanks. - Nov 10th 2012, 09:40 PMProve ItRe: Factoring help
Start by letting , then the equation becomes . This doesn't factorise over the integers, but does factorise over the real numbers by completing the square.

- Nov 10th 2012, 10:42 PMgfbrdRe: Factoring help
I completed the square and got

(x-49)^2 +2400

what do I do next? - Nov 10th 2012, 10:43 PMProve ItRe: Factoring help
That can't possibly be right - expand it out and check...

- Nov 10th 2012, 10:58 PMgfbrdRe: Factoring help
sorry it should be -2400

(x-49)^2 - 2400 = (x-49)(x-49) - 2400 = x^2 -49x - 49x + 2401 -2400 = x^2 - 98x + 1

ok so when completing the square i get

(x-49)^2 - 2400

what do I do next? - Nov 10th 2012, 11:01 PMProve ItRe: Factoring help
Write it as and then use the Difference of Two Squares rule to factorise it.

- Nov 10th 2012, 11:27 PMgfbrdRe: Factoring help
so it is ((x-49)^2 + (20sqrt(6))^2)((x-49)^2 - (20sqrt(6))^2))

what do I do from here? - Nov 11th 2012, 09:58 AMSorobanRe: Factoring help
Hello, gfbrd!

This takes a little Imagination . . .

Quote:

Factor into two non-constant polynomials with integral coefficients.

- Nov 11th 2012, 10:11 AMgfbrdRe: Factoring help
lol sorry my imagination isn't really as good as yours

thanks a lot soroban