[Blindmath] Help factoring a crazy trinomial

[Susan Osterhaus]

I definitely think it was a typo.

x⁴-2x²+1 = (x+1)(x-1)(x+1)(x-1) = (x-1)²(x+1)² = (x²-1)² = (x²-1)(
x²-1) or

x^(4)-2x^(2)+1 = (x+1)(x-1)(x+1)(x-1) = ((x-1)^(2))((x+1)^(2)) = (x^(2)-
1)^2 = (x^(2)-1)(x^(2)-1)

I think this last factorization is what you were looking for when you
said " four termed expression where the product of the first and last
terms must equal  the product of the two middle terms." I think you want
to use a factoring technique.

The original trinomial is what is called a perfect square trinomial, and
it can be solved by factoring. The general case is as follows:
a²-2ab+b² = (a-b)² or
a^(2)-2ab+b^(2) = (a-b)^2

I hope this is what you were trying to remember.

Susan


-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Jon
Yaggie
Sent: Wednesday, October 23, 2013 2:13 PM
To: GianniP46; Blind Math list for those interested in mathematics
Subject: Re: [Blindmath] Help factoring a crazy trinomial

Note if it was a typo.  And it should have been x^2 - 2x +1.  You still
would solve it by the substitution. Or synthetic division if you know a
root.

Jon Yaggie


> On Oct 23, 2013, at 13:49, "GianniP46" <giannip46 at earthlink.net> wrote:
>
> Hi all,
> I need help factoring X^4-2X^2-1
>
> I am thinking that there is a way of re writing this as a four termed
> expression where the product of the first and last terms must equal
> the product of the two middle terms, but I am stuck :( I know the
> answer is (X+1)(X-1)(X+1)(X-1) Feeling very dumb, any help would be
> appreciated THANKS lol
>
> Gian Pedulla
> Giannip46 at earthlink.net
>
> LETS GO METS!
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