Question

Divide x4 - 6x3 + x2 + 138x - 35 by x2 - 4x + 1

Answer 1

x4+x2+138x-53/x2-4x+1

Answer 2

`x^(4)-6x^(3)+x^(2)+138x-35x^(2)-4x-6x^(3)-34x^(2)+134x+1`

Steps:

`x^(4)-6x^(3)+x^(2)+138x-35x^(2)-4x+1`

Group like terms:

`x^(4)-6x^(3)+x^(2)-35x^(2)+138x-4x+1`

Add similar elements: 138x-4x=134x

`x^(4)-6x^(3)+x^(2)-35x^(2)+134x+1`

Add similar elements: x^2-35x^2=-34x^2

`x^(4)-6x^(3)+x^(2)-35x^(2)+134x+1`