Question

How do you use polynomial synthetic division to divide `(x^6-6x^4+12x^2-8)div(x+sqrt2)` and write the polynomial in the form `p(x)=d(x)q(x)+r(x)`?

Answer 1

`q(x) = x^5 - x^4 sqrt 2 -4 x^3 + 4 x^2 sqrt 2 + 20 x - 20 sqrt 2`
`r(x) = 32`

Explanation:

Briot Ruffini

`((),(-sqrt 2)) ((1),(1)) ((0),(-sqrt 2)) ((-6),(-4)) ((0),(4 sqrt 2)) ((12),(20)) ((0),(- 20 sqrt 2)) ((-8),(32))`

`p(x)=d(x)q(x)+r(x)`

`d(x) = x + sqrt 2`

`q(x) = x^5 - x^4 sqrt 2 -4 x^3 + 4 x^2 sqrt 2 + 20 x - 20 sqrt 2`

`r(x) = 32`