Question

factorise x2+1/x2+2-2x-2/x. after the variable it is square.means raise to 2.

Answer 1

X^2+1/x^2+2-2x-2/x=0

(X^4+1+2x^2-2x^3-2x)/x^2=0

Let,p(x)=x^4-2x^3+2x^2-2x+1=0

Let,x=1

(1)^4-2(1)^3+2(1)^2-2(1)+1

1+1+2-2-2

=0

Therefore,(x-1) is a factor of p(x).

Now,

(x^4-2x^3+2x^2-2x+1)/x-1

Therefore remainder =0and quotient= x^3-x^2+x-1

Now, x^3-x^2+x-1=0

Let x=1

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

=0

Therefore, (x-1) is a factor of x^3-x^2+x-1.

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

Remainder=0, quotient =x^2+1

Now, x^2+1=0

1=-x^2

X=-1

Therefore (x-1) is a factor of x^4-2x^3+2x^2-2x+1.