Question

The H.C.F. of the expressions x4+3x2-4 and x4-4x2+3 is ​

Answer 1

Answer:

1st term

x^4+3x^2-4

=x^4+4x^2-x^2-4

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

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

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

2nd term

x^4-4x^2+3

=x^4-3x^2-x^2+3

=x^2(x^2-3)-1(x^2-3)

=(x^2-3)(x^2-1)

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

so, HCF of the above two expression s

(x+1)(x-1)

=x^2-1