Factorising (1 Viewer)

[mathyics]

Just wondering how to factorize this (2x^4-3x^2+x)^1/2

would that be x^1/2(2x^3-3x+1)^1/2 or x(2x^3-3x+1)^1/2 or neither?

 

[CheesePlease]

Hmm, not 100% sure, but I'd say.

 

[mirakon]

Hmm, not 100% sure, but I'd say.

Not entirely as the zeroes are all

x= 1
x= 0
x= (-1+3^1/2)/2
x= (-1-3^1/2)/2

So that answer is not fully factorised.

Fully Factorised is

(x(x-1)(x+(1-3^1/2)/2)(2x+(1+3^1/2))^1/2

Although check it as I did it in my head

 

[hscishard]

The 2nd seems right but I think you can factorise it even further.
You can use a 3unit method or an unfamilar 2 unit method.

 

[hscishard]

Not entirely as the zeroes are all

x= 1
x= 0
x= (-1+3^1/2)/2
x= (-1-3^1/2)/2

So that answer is not fully factorised.

Fully Factorised is

(x(x-1)(x+(1-3^1/2)/2)(2x+(1+3^1/2))^1/2

Although check it as I did it in my head

Hmmm.. I got x(x-1)(2x^2+2x-1)

 

[mirakon]

Hmmm.. I got x(x-1)(2x^2+2x-1)

Yeah, but I factorised the 2x^2+2x-1 further.

Also, don't forget the square root!

 

[hscishard]

Yeah, but I factorised the 2x^2+2x-1 further.

Also, don't forget the square root!

I know, I just wanted to show the main part. How can you factorise it further? It would be in surd form, wouldn't it?

OHhh yea, you did factorise to surd form. Nice